Search

In this article, we study Galois points of plane curves and the extension of the corresponding Galois group to $\mathrm{Bir}(\mathbb{P}^2)$. We prove that if the Galois group has order at most $3$ , it always extends to a subgroup of the Jonquières group associated with the point $P$. Conversely, with a degree of at least $4$ , we prove that it is false. We provide an example of a Galois extension whose Galois group is extendable to Cremona transformations but not to a group of de Jonquières maps with respect to $P$. In addition, we also give an example of a Galois extension whose Galois group cannot be extended to Cremona transformations. [ABSTRACT FROM AUTHOR]

For prime p and small n , Jones and Roberts have developed a database recording invariants for p -adic extensions of degree n. We contributed to this database by computing the Galois slope content, Galois mean slope, and inertia subgroup for a variety of wildly ramified extensions of composite degree using the idea of Galois splitting models. We will describe a number of strategies to find Galois splitting models including an original technique using generic polynomials and Panayi's root finding algorithm. [ABSTRACT FROM AUTHOR]

For positive integers n ≥ m , let P n , m (x) : = ∑ j = 0 m n j x j = n 0 + n 1 x + ... + n m x m be the truncated binomial expansion of (1 + x) n consisting of all terms of degree ≤ m. It is conjectured that for n > m + 1 , the polynomial P n , m (x) is irreducible. We confirm this conjecture when 2 m ≤ n < (m + 1) 1 0. Also we show for any r ≥ 1 0 and 2 m ≤ n < (m + 1) r + 1 , the polynomial P n , m (x) is irreducible when m ≥ max { 1 0 6 , 2 r 3 }. Under the explicit abc-conjecture, for a fixed m , we give an explicit n 0 , n 1 depending only on m such that ∀ n ≥ n 0 , the polynomial P n , m (x) is irreducible. Further ∀ n ≥ n 1 , the Galois group associated to P n , m (x) is the symmetric group S m. [ABSTRACT FROM AUTHOR]

Jambor–Liebeck–O'Brien showed that there exist non-proper-power word maps which are not surjective on PSL 2 (F q) for infinitely many q. This provided the first counterexamples to a conjecture of Shalev which stated that if a two-variable word is not a proper power of a non-trivial word, then the corresponding word map is surjective on PSL 2 (F q) for all sufficiently large q. Motivated by their work, we construct new examples of these types of non-surjective word maps. As an application, we obtain non-surjective word maps on the absolute Galois group of Q , and on SL 2 (K) where K is a number field of odd degree. [ABSTRACT FROM AUTHOR]

We achieve several results. First, we develop a variant of the theory of absolute Galois groups in the context of many sorted structures. Second, we provide a method for coding absolute Galois groups of structures, so they can be interpreted in some monster model with an additional predicate. Third, we prove the "Weak Independence Theorem" for pseudo-algebraically closed (PAC) substructures of an ambient structure with no finite cover property (nfcp) and the property B (3). Fourth, we describe Kim-dividing in these PAC substructures and show several results related to the SOPn hierarchy. Fifth, we characterize the algebraic closure in PAC structures. [ABSTRACT FROM AUTHOR]

In this paper we discuss applications of our earlier work in studying certain Galois groups and splitting fields of rational functions in Q (X 0 (N)) using Hilbert's irreducibility theorem and modular forms. We also consider computational aspect of the problem using MAGMA and SAGE. [ABSTRACT FROM AUTHOR]

Let f (x) = x 8 + a x 4 + b ∈ ℚ [ x ] be an irreducible polynomial where b is a square. We give a method that completely describes the factorization patterns of a linear resolvent of f (x) using simple arithmetic conditions on a and b. As a result, we determine the exact six possible Galois groups of f (x) and completely classify all of them. As an application, we characterize the Galois groups of irreducible polynomials x 8 + a x 4 + 1 ∈ ℚ [ x ]. We also use similar methods to obtain analogous results for the Galois groups of irreducible polynomials x 8 + a x 6 + b x 4 + a x 2 + 1 ∈ ℚ [ x ]. [ABSTRACT FROM AUTHOR]

Galois groups distinguish the part of 3d electrons in a volume of 'orbital glass' (OG). That renormalizes spectrum εk of band fermions. Increasing of their mass Δεk (Lr) ≅ 0.1 eV increases effective mass of d fermions by Δm* ≈ (1-10)m* for part of 3d band in the OG volume. The value of orbital moment decreases (L < 1) that explains measured orbital moments of 3d ions (Co, Ni, etc.). [ABSTRACT FROM AUTHOR]

Hardness (MH) is calculated by means of the method of many-electron operator spinors as phase transition with formation of 'orbital glass'. Indenter pressure PJ overcomes (internal) binding forces Eel (band, covalent ones, etc.). 'Orbital glass' energy EOG is the largest in precious stones and metals (PMH ≈ EOG >> Eel). Magnetic field Bz under transition, side by side with deformation u33, draws up segregation Lr||Oz--Galois group G33. In large fields Bz > Bcr, domain walls Lzr degenerate into asymmetrical phases (amorphous carbon). These are defects of diamond crystal. [ABSTRACT FROM AUTHOR]

We study the relation between the Galois group G of a linear difference-differential system and two classes C 1 and C 2 of groups that are the Galois groups of the specializations of the linear difference equation and the linear differential equation in this system respectively. We show that almost all groups in C 1 ∪ C 2 are algebraic subgroups of G , and there is a nonempty subset of C 1 and a nonempty subset of C 2 such that G is the product of any pair of groups from these two subsets. These results have potential application to the computation of the Galois group of a linear difference-differential system. We also give a criterion for testing linear dependence of elements in a simple difference-differential ring, which generalizes Kolchin's criterion for partial differential fields. [ABSTRACT FROM AUTHOR]

We describe algorithms to compute splitting fields and towers of radical extensions in which a polynomial splits, without using polynomial factorisation in towers or constructing any field properly containing the constructed field, instead extending Galois group computations for this task. We also describe the computation of geometric Galois groups (monodromy groups) and their use in computing absolute factorizations. [ABSTRACT FROM AUTHOR]

We study the Galois groups of polynomials arising from a compatible family of representations with big orthogonal monodromy. We show that the Galois groups are usually as large as possible given the constraints imposed on them by a functional equation and discriminant considerations. As an application, we consider the Frobenius polynomials arising from the middle étale cohomology of hypersurfaces in ℙ q 2 n + 1 of degree at least three. We also consider the L -functions of quadratic twists of fixed degree of an elliptic curve over a function field q (t). To determine the typical Galois group in the elliptic curve setting requires using some known cases of the Birch and Swinnerton-Dyer conjecture. This extends and generalizes work of Chavdarov, Katz and Jouve. [ABSTRACT FROM AUTHOR]

Key words and phrases: In this paper by exploiting the properties of transitive permutation groups of prime degree we provide an answer to the following problem: given two number fields K and L both of prime degree p over Q, what values the degree of their compositum KL can take? We show that if K and L are linearly disjoint over Q, then necessarily KL has degree p² or, for example, if K and L are number fields of prime degree p such that p = (qn-1)/(q-1) with q prime or a power of a prime, n≥3, and some intermediate group between the projective special linear group PSL(n,q) and the projective semilinear group PΓL(n,q) is realizable over Q, then the degree of KL is pqn-1. In addition, for any divisor s of p-1, there exist number fields K and L of prime degree p such that their compositum KL has degree ps. As a numerical application, we determine the complete list of values the degree of compositum KL can take if K and L are two number fields of degree 13. We also give an answer to the related problem, namely, given two algebraic numbers α and β both of prime degree p, what values the degree of α+β and αβ can take? [ABSTRACT FROM AUTHOR]

We give a classification of the generalized Laguerre polynomials L n (α) (x) , where α ≠ n is an integer, having the alternating group A n as the Galois group over the rationals for up to a finitely many exceptions. [ABSTRACT FROM AUTHOR]

We show that for some recursive sequence (c m) m ≥ 1 of integers and for sufficiently large n, the Galois group of polynomial f n (x) = x n n ! + c n - 1 x n - 1 (n - 1) ! + ⋯ + c 1 x 1 ! + 1 , contains the alternating group A n . In case n is a prime number, this group is the full symmetric group S n . [ABSTRACT FROM AUTHOR]

Recently, two-to-one mappings have received a lot of attention due to their applications to cryptography and to the construction of classes of cryptographic functions. In this paper, we propose a new method to obtain m -to-1 functions based on Galois groups of rational functions. We feel that such an approach might be the starting point of a new line of research in the area of m -to-1 mappings. [ABSTRACT FROM AUTHOR]

We create plots of algebraic integers in the complex plane, exploring the effect of sizing the points according to various arithmetic invariants. We focus on Galois theoretic invariants, in particular creating plots which emphasize algebraic integers whose Galois group is not the full symmetric group−these integers we call rigid. We then give some analysis of the resulting images, suggesting avenues for future research about the geometry of so-called rigid algebraic integers. [ABSTRACT FROM AUTHOR]

We prove a result on the asymptotic proportion of randomly chosen pairs (σ , τ) of permutations in the symmetric group S n which "invariably" generate a nonsolvable subgroup, i.e., whose cycle structures cannot possibly both occur in the same solvable subgroup of S n . As an application, we obtain that for a large degree "random" integer polynomial f, reduction modulo two different primes can be expected to suffice to prove the nonsolvability of Gal (f / Q) . [ABSTRACT FROM AUTHOR]

Let P ∈ Q [ t , x ] be a polynomial in two variables with rational coefficients, and let G be the Galois group of P over the field Q (t). It follows from Hilbert's Irreducibility Theorem that for most rational numbers c the specialized polynomial P (c , x) has Galois group isomorphic to G and factors in the same way as P. In this paper we discuss methods for computing the group G and obtaining an explicit description of the exceptional numbers c , i.e., those for which P (c , x) has Galois group different from G or factors differently from P. To illustrate the methods we determine the exceptional specializations of three sample polynomials. In addition, we apply our techniques to prove a new result in arithmetic dynamics. [ABSTRACT FROM AUTHOR]

In this paper, we study the actions of profinite groups on Cantor sets which arise from representations of Galois groups of certain fields of rational functions. Such representations are associated to polynomials, and they are called profinite iterated monodromy groups. We are interested in a topological invariant of such actions called the asymptotic discriminant. In particular, we give a complete classification by whether the asymptotic discriminant is stable or wild in the case when the polynomial generating the representation is quadratic. We also study different ways in which a wild asymptotic discriminant can arise. [ABSTRACT FROM AUTHOR]

For any finite Galois field extension K/F, with Galois group G = Gal (K/F), there exists an element α ∈ K whose orbit G · α forms an F-basis of K. Such an α is called a normal element, and G · α is a normal basis. We introduce a probabilistic algorithm for testing whether a given α ∈ K is normal, when G is either a finite abelian or a metacyclic group. The algorithm is based on the fact that deciding whether α is normal can be reduced to deciding whether ∑ g ∈ G g (α) g ∈ K[G] is invertible; it requires a slightly subquadratic number of operations. Once we know that α is normal, we show how to perform conversions between the power basis of K/F and the normal basis with the same asymptotic cost. [ABSTRACT FROM AUTHOR]

We present the (Lascar) Galois group of any countable theory as a quotient of a compact Polish group by an F σ normal subgroup: in general, as a topological group, and under NIP, also in terms of Borel cardinality. This allows us to obtain similar results for arbitrary strong types defined on a single complete type over ∅. As an easy conclusion of our main theorem, we get the main result of [K. Krupiński, A. Pillay and T. Rzepecki, Topological dynamics and the complexity of strong types, Israel J. Math.228 (2018) 863–932] which says that for any strong type defined on a single complete type over ∅ , smoothness is equivalent to type-definability. We also explain how similar results are obtained in the case of bounded quotients of type-definable groups. This gives us a generalization of a former result from the paper mentioned above about bounded quotients of type-definable subgroups of definable groups. [ABSTRACT FROM AUTHOR]

We generalize a well-known theorem binding the elementary equivalence relation on the level of PAC fields and the isomorphism type of their absolute Galois groups. Our results concern two cases: saturated PAC structures and nonsaturated PAC structures. [ABSTRACT FROM AUTHOR]

We study modulo p reduction of compatible systems of p -adic representations of the absolute Galois group of Q , arising from an algebraic automorphic representation. In particular, we prove that there is a field extension of Q with the Galois group G 2 (p) , ramified at 5 and p only, for a set of primes p of density one. [ABSTRACT FROM AUTHOR]

Abstract For a prime number p , we give a new restriction on pro- p groups G which are realizable as the maximal pro- p Galois group G F (p) for a field F containing a root of unity of order p. This restriction arises from Kummer Theory and the structure of the maximal p -radical extension of F. We study it in the abstract context of pro- p groups G with a continuous homomorphism θ : G → 1 + p Z p , and characterize it cohomologically, and in terms of 1-cocycles on G. This is used to produce new examples of pro- p groups which do not occur as maximal pro- p Galois groups of fields as above. [ABSTRACT FROM AUTHOR]

Let K be an arbitrary field of characteristic zero with an absolute value on it. We show that if F and G are monic and normal polynomials of of the same degree with coefficients close enough to each other with respect to this absolute value, then the Galois groups of the splitting fields of F and G over K are isomorphic. We point out a quantitative result and discuss some special cases and related problems. [ABSTRACT FROM AUTHOR]

Copyright of Metallophysics & Advanced Technologies / Metallofizika i Novejsie Tehnologii is the property of G.V. Kurdyumov Institute for Metal Physics, N.A.S.U and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this note we make some remarks on the classical Laguerre’s theorem and extend it and some other old results of Walsh and Gauss-Lucas to the so called trace series associated with transcendental elements of the completion of the algebraic closure of Q in C, with respect to the spectral norm:

Much of arithmetic geometry is concerned with the study of principal bundles. They occur prominently in the arithmetic of elliptic curves and, more recently, in the study of the Diophantine geometry of curves of higher genus. In particular, the geometry of moduli spaces of principal bundles holds the key to an effective version of Faltings' theorem on finiteness of rational points on curves of genus at least 2. The study of arithmetic principal bundles includes the study of Galois representations, the structures linking motives to automorphic forms according to the Langlands program. In this paper, we give a brief introduction to the arithmetic geometry of principal bundles with emphasis on some elementary analogies between arithmetic moduli spaces and the constructions of quantum field theory. [ABSTRACT FROM AUTHOR]

We establish several surjectivity theorems regarding the Galois groups of small iterates of ϕc(x)=x2+c for c∈ℚ. To do this, we use explicit techniques from the theory of rational points on curves, including the method of Chabauty–Coleman and the Mordell–Weil sieve. For example, we succeed in finding all rational points on a hyperelliptic curve of genus 7, with rank 5 Jacobian, whose points parametrize quadratic polynomials with a “newly small” Galois group at the fifth stage of iteration. [ABSTRACT FROM AUTHOR]

We study the algebraic properties of Generalized Laguerre polynomials for negative integral values of a given parameter which is L n ( − 1 − n − r ) ( x ) = ∑ j = 0 n ( n − j + r n − j ) x j j ! for integers r ≥ 0 , n ≥ 1 . For different values of parameter r , this family provides polynomials which are of great interest. Hajir conjectured that for integers r ≥ 0 and n ≥ 1 , L n ( − 1 − n − r ) ( x ) is an irreducible polynomial whose Galois group contains A n , the alternating group on n symbols. Extending earlier results of Schur, Hajir, Sell, Nair and Shorey, we confirm this conjecture for all r ≤ 60 . We also prove that L n ( − 1 − n − r ) ( x ) is an irreducible polynomial whose Galois group contains A n whenever n > e r ( 1 + 1.2762 log r ) . [ABSTRACT FROM AUTHOR]

Let $$\varphi _p(z)=(z-1)^p+2-\zeta _p$$ , where $$\zeta _p\in \bar{\mathbb {Q}}$$ is a primitive pth root of unity. Building on previous work, we show that the nth iterate $$\varphi _p^n(z)$$ has Galois group $$[C_p]^n$$ , an iterated wreath product of cyclic groups, whenever p is not a Wieferich prime. [ABSTRACT FROM AUTHOR]

It is proved in this paper that any preassigned system of five and more than five finite quantity squares with total area 1 may be packed in parallel into a rectangle whose area is at least S d =(2 + 3 1/2 )/3. [ABSTRACT FROM AUTHOR]

This paper is a greatly expanded version of [37, Section 9.11] . A series of definitions and results illustrating the thesis in the title (where quasi-formality means vanishing of a certain kind of Massey multiplications in the cohomology) is presented. In particular, we include a categorical interpretation of the “Koszulity implies K ( π , 1 ) ” claim, discuss the differences between two versions of Massey operations, and apply the derived nonhomogeneous Koszul duality theory in order to deduce the main theorem. In the end we demonstrate a counterexample providing a negative answer to a question of Hopkins and Wickelgren about formality of the cochain DG-algebras of absolute Galois groups, thus showing that quasi-formality cannot be strengthened to formality in the title assertion. [ABSTRACT FROM AUTHOR]

Let K be a field whose characteristic is prime to a fixed positive integer n such that µn ⊂ K, and choose ω ∈ µn as a primitive n-th root of unity. Denote the absolute Galois group of K by Gal(K), and the mod-n central-descending series of Gal(K) by Gal(K)(i). Recall that Kummer theory, together with our choice of ω, provides a functorial isomorphism between Gal(K)/ Gal(K)(2) and Hom(K×, ℤ/n). Analogously to Kummer theory, in this note we use the Merkurjev-Suslin theorem to construct a continuous, functorial and explicit embedding Gal(K)(2)/ Gal(K)(3) → Fun(K \ {0,1}, (ℤ/n)2), where Fun(K \ {0,1}, (ℤ/n)2) denotes the group of (ℤ/n)2-valued functions on K \ {0,1}. We explicitly determine the functions associated to the image of commutators and n-th powers of elements of Gal(K) under this embedding. We then apply this theory to prove some new results concerning relations between elements in abelian-by-central Galois groups. [ABSTRACT FROM AUTHOR]

We study the Oort groups for a prime p , i.e. finite groups G such that every G -Galois branched cover of smooth curves over an algebraically closed field of characteristic p lifts to a G -cover of curves in characteristic 0. We prove that all Oort groups lie in a particular class of finite groups that we characterize, with equality of classes under a conjecture about local liftings. We prove this equality unconditionally if the order of G is not divisible by 2 p 2 . We also treat the local lifting problem and relate it to the global problem. [ABSTRACT FROM AUTHOR]

For any prime p and positive integers c, d there is up to isomorphism a unique p-group $${G_{d}^{c}(p)}$$ of least order having any (finite) p-group G with rank $${d(G) \le d}$$ and Frattini class $${c_{p}(G) \le c}$$ as epimorphic image. Here $${c_{p}(G) = n}$$ is the least positive integer such that G has a central series of length n with all factors being elementary. This 'disposition' p-group $${G_{d}^{c}(p)}$$ has been examined quite intensively in the literature, sometimes controversially. The objective of this paper is to present a summary of the known facts, and to add some new results. For instance we show that for $${G = G_{d}^{c}(p)}$$ the centralizer $${C_{G}(x) = \langle Z(G), x \rangle}$$ whenever $${x \in G}$$ is outside the Frattini subgroup, and that for odd p and $${d \ge 2}$$ the group $${E = G_{d}^{c+1}(p)/(G_{d}^{c+1}(p))^{p^{c}}}$$ is a distinguished Schur cover of G with $${E/Z(E) \cong G}$$ . We also have a fibre product construction of $${G_{d}^{c+1}(p)}$$ in terms of $${G = G_{d}^{c}(p)}$$ which might be of interest for Galois theory. [ABSTRACT FROM AUTHOR]

Let $F$ be a finite extension of $Bbb Q$, ${Bbb Q}_p$ or a globalfield of positive characteristic, and let $E/F$ be a Galois extension.We study the realization fields offinite subgroups $G$ of $GL_n(E)$ stable under the naturaloperation of the Galois group of $E/F$. Though for sufficiently large $n$ and a fixedalgebraic number field $F$ every its finite extension $E$ isrealizable via adjoining to $F$ the entries of allmatrices $gin G$ for some finite Galois stable subgroup $G$ of $GL_n(Bbb C)$, there is only afinite number of possible realization field extensions of $F$ if $Gsubset GL_n(O_E)$ over thering $O_E$ of integers of $E$. After an exposition of earlier results we give their refinementsfor therealization fields $E/F$. We consider some applications to quadratic lattices, arithmetic algebraic geometry and Galois cohomology of related arithmetic groups.

Let A be a unital associative algebra over a field k. All unital associative algebras containing A as a subalgebra of a given codimension $$\mathfrak {c}$$ are described and classified. For a fixed vector space V of dimension $$\mathfrak {c}$$ , two non-abelian cohomological type objects are explicitly constructed: $${\mathcal {A}}{{\mathcal {H}}}^{2}_{A} \, (V, \, A)$$ will classify all such algebras up to an isomorphism that stabilizes A while $${\mathcal {A}}{{\mathcal {H}}}^{2} \, (V, \, A)$$ provides the classification from Hölder's extension problem viewpoint. A new product, called the unified product, is introduced as a tool of our approach. The classical crossed product or the twisted tensor product of algebras are special cases of the unified product. Two main applications are given: the Galois group $$\mathrm{Gal} \, (B/A)$$ of an extension $$A \subseteq B$$ of associative algebras is explicitly described as a subgroup of a semidirect product of groups $$\mathrm{GL}_k (V) \rtimes \mathrm{Hom}_k (V, \, A)$$ , where the vector space V is a complement of A in B. The second application refers to supersolvable algebras introduced as the associative algebra counterpart of supersolvable Lie algebras. Several explicit examples are given for supersolvable algebras over an arbitrary base field, including those of characteristic two whose difficulty is illustrated. [ABSTRACT FROM AUTHOR]

We consider the arithmetic background of integral representations of finite groups over -adic and algebraic number rings. Some infinite series of integral pairwise inequivalent absolutely irreducible representations of finite -groups with the extra congruence conditions are constructed, and some applications are given. Certain problems concerning integral irreducible two-dimensional representations over number rings are discussed. [ABSTRACT FROM AUTHOR]

Text Let k be a field containing F q . Let ψ be a rank r Drinfeld F q [ t ] -module determined by ψ t ( X ) = t X + a 1 X q + ⋯ + a r − 1 X q r − 1 + X q r , where t , a 1 , … , a r − 1 are algebraically independent over k . Let n ∈ F q [ t ] be a monic polynomial. We show that the Galois group of ψ n ( X ) over k ( t , a 1 , … , a r − 1 ) is isomorphic to GL r ( F q [ t ] / n F q [ t ] ) , settling a conjecture of Abhyankar. Along the way we obtain an explicit construction of Drinfeld moduli schemes of level tn . Video For a video summary of this paper, please visit https://youtu.be/TInrNq02-UA . [ABSTRACT FROM AUTHOR]

We describe a general algorithm for the computation of Galois groups of polynomials over global fields from the point of view of using it to compute Galois groups of polynomials over function fields with prime characteristic, including characteristic 2 in which some invariants which are efficient to use in other characteristics are invariant for too large a group. We state new invariants for most of these situations when the characteristic is 2. We also describe the use of this algorithm for computing Galois groups of reducible polynomials over both number fields and function fields. [ABSTRACT FROM AUTHOR]

We show that the Galois group of any Schubert problem involving lines in projective space contains the alternating group. This constitutes the largest family of enumerative problems whose Galois groups have been largely determined. Using a criterion of Vakil and a special position argument due to Schubert, our result follows from a particular inequality among Kostka numbers of two-rowed tableaux. In most cases, a combinatorial injection proves the inequality. For the remaining cases, we use the Weyl integral formulas to obtain an integral formula for these Kostka numbers. This rewrites the inequality as an integral, which we estimate to establish the inequality. [ABSTRACT FROM AUTHOR]

We study arithmetic problems for representations of finite groups over algebraic number fields and their orders under the ground field extensions. Let $$E/F$$ be a Galois extension, and let $$G\subset GL_n(E)$$ be a subgroup stable under the natural operation of the Galois group of $$E/F$$ . A concept generalizing permutation modules is used to determine the structure of groups $$G$$ and their realization fields. We also compare the possible realization fields of $$G$$ in the cases if $$G\subset GL_n(E)$$ , and if all coefficients of matrices in $$G$$ are algebraic integers. Some related results and conjectures are considered. [ABSTRACT FROM AUTHOR]

A finite groupGis called admissible over a given field if there exists a central division algebra that contains aG-Galois field extension as a maximal subfield. We give a definition of embedding problems of division algebras that extends both the notion of embedding problems of fields as in classical Galois theory, and the question which finite groups are admissible over a field. In a recent work by Harbater, Hartmann, and Krashen, all admissible groups over function fields of curves over complete discretely valued fields with algebraically closed residue field of characteristic zero have been characterized. We show that also certain embedding problems of division algebras over such a field can be solved for admissible groups. [ABSTRACT FROM AUTHOR]