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Abstract We compute the group of K 1 -zero-cycles on the second generalized involution variety for an algebra of degree 4 with symplectic involution. This description is given in terms of the group of multipliers of similitudes associated to the algebra with involution. Our method utilizes the framework of Chernousov and Merkurjev for computing K 1 -zero-cycles in terms of R -equivalence classes of prescribed algebraic groups. This gives a computation of K 1 -zero-cycles for some homogeneous varieties of type C 2. [ABSTRACT FROM AUTHOR]

We show that the cohomology ring of Hilbert scheme of n-points in the affine plane is isomorphic to the coordinate ring of a Gm-fixed point scheme of the n-th symmetric product of C2 for a natural Gm-action on it. This result can be seen as an analogue of a theorem of DeConcini-Procesi and Tanisaki on a description of the cohomology ring of Springer fiber of type A. We also prove similar results for type A S3-varieties and smooth hypertoric varieties. These results can be formulated in terms of the symplectic duality of Braden-Licata-Proudfoot-Webster. [ABSTRACT FROM AUTHOR]

As a first step in a general verification of the Alperin-McKay conjecture, we prove a reduction of the conjecture to statements about simple groups. Furthermore we show in numerous cases, that simple groups satisfy the required conditions. The methods are also applied to obtain similar results for refinements due to Isaacs and Navarro. [ABSTRACT FROM AUTHOR]

We provide a family of counterexamples to a first formulation of the dynamical Manin–Mumford conjecture. We propose a revision of this conjecture and prove it for arbitrary subvarieties of Abelian varieties under the action of group endomorphisms and for lines under the action of diagonal endomorphisms of . [ABSTRACT FROM PUBLISHER]

Berkovich (Invent. Math. 125(2):367–390, ), Fujiwara (Duke Math. J. 80(1):15–57, ) and Huber (J. Algebraic Geom. 7(2):359–403, ) have proved that the fiber of the vanishing cycles at a point of the special fiber depends only on the formal completion at this point. We refine this result and prove the invariance under formal completion of the perverse monodromy filtration on the fiber of vanishing cycles. This result is used in an essential way by Boyer (Invent. Math. doi:, ). [ABSTRACT FROM AUTHOR]

We consider adequate transversals of abundant semigroups and prove that, in a particular case, there is a natural embedding of an inverse transversal within a certain regular subsemigroup. We also introduce the concepts of simplistic, perfect, and quasi-adequate transversal and provide a number of interesting connections between these. [ABSTRACT FROM AUTHOR]

AbstractIn this paper we present Thom?s transversality theorem in o-minimal structures (a generalization of semialgebraic and subanalytic geometry). There are no restrictions on?the differentiability class and the dimensions of manifolds involved in comparison withthe general case. [ABSTRACT FROM AUTHOR]

This paper concerns involutions and anti-automorphisms on finite-dimensional associative algebras over a field. It is based on a survey talk given at the workshop on ‘Quadratic forms, algebras with involution and algebraic K-theory’ at the University of Nottingham, 13–15 May 2004. This workshop was part of the EU network HPRN-CT-2002-00287 on ‘Algebraic $K$-theory, linear algebraic groups and related structures’ and followed the London Mathematical Society Midlands Regional Meeting in Nottingham on 12 May, 2004.The contents of the article are as follows:Introduction and historical remarks;Some general results;Central simple algebras;Group algebras. [ABSTRACT FROM AUTHOR]

The main aim of this paper is to construct the character tables of the parabolic subgroups of the Chevalley groups G 2 ( q ), where q is a power of a prime p > 3. [ABSTRACT FROM AUTHOR]

We explain how to adapt a construction due to M. Sageev in order to construct a proper action of a group on a CAT(0) cube complex starting from a proper action of the group on a wall space. [ABSTRACT FROM AUTHOR]

In the present paper, we give a first general construction of compactified moduli spaces for semistable G-bundles on an irreducible complex projective curve X with exactly one node, where G is a semisimple linear algebraic group over the complex numbers. [ABSTRACT FROM AUTHOR]

A classification is given of all spreads in PG(3, q), q = p r, p odd, whose associated translation planes admit linear collineation groups of order q( q +1) such that a Sylow p-subgroup fixes a line and acts non-trivially on it. [ABSTRACT FROM AUTHOR]

A concept of higher order complexity is proposed in this letter. If a randomness-finding complexity [Rapp & Schmah, 2000] is taken as the complexity measure, the first-order complexity is suggested to be a measure of randomness of the original time series, while the second-order complexity is a measure of its degree of nonstationarity. A different order is associated with each different aspect of complexity. Using logistic mapping repeatedly, some quasi-stationary time series were constructed, the nonstationarity degree of which could be expected theoretically. The estimation of the second-order complexity of these time series shows that the second-order complexities do reflect the degree of nonstationarity and thus can be considered as its indicator. It is also shown that the second-order complexities of the EEG signals from subjects doing mental arithmetic are significantly higher than those from subjects in deep sleep or resting with eyes closed. [ABSTRACT FROM AUTHOR]

We study the subgroup B0(G) of H²(G, &doubleQ;/&doubleZ;) consisting of all elements which have trivial restrictions to every Abelian subgroup of G. The group B0(G) serves as the simplest nontrivial obstruction to stable rationality of algebraic varieties V/G where V is a faithful complex linear representation of the group G. We prove that B0(G) is trivial for finite simple groups of Lie type Aℓ. [ABSTRACT FROM AUTHOR]

The nonprimary subgroups of the symmetric group S9 are investigated. Embedding properties of these subgroups are listed in a table. Properties such as abnormality, pronormality, paranormality, weak normality, etc. were checked with the help of a computer. Algorithms and codes of the first author were used for this purpose. The research leans upon the technique of Burnside marks, as well as upon pertinent information on the table of marks of S9 from the computer algebra package GAP. The subgroups were investigated up to conjugacy; the total number of conjugacy classes of nonprimary subgroups of S9 is 432. Some subgroups were additionally checked by other programs based on the double coset method. Bibliography: 24 titles. [ABSTRACT FROM AUTHOR]

The paper is devoted to a description of the pairs of unipotent short root subgroups in the Chevalley group of type G2 over a field of characteristic different from 2. Namely, the subgroups generated by a pair of short root subgroups are described, and the orbits of the Chevalley group, which acts by simultaneous conjugation on such pairs, are classified. Most of the calculations are valid for fields of characteristic 2. Bibliography: 14 titles. [ABSTRACT FROM AUTHOR]

In this article we prove Broué's conjecture on isotypies for the case of principal blocs of Sp(4, Fq)〈σ〉 : a split cyclic extension of the symplectic group of dimension 4 over a finite field Fq for q odd. The core of the proof is to lift to the group Sp(4, Fq)〈σ〉 an isotypy of the group Sp(4, Fq). For this purpose, we build a convenient version of a theorem of lifting isotypies. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring with 1, let 2 ∈ R*, and let l ≥ 3. We describe the subgroups of the general linear group GL(n,R) that contain the split elementary orthogonal group EO(2l,R). For every intermediate subgroup H, there exists a unique maximal ideal A ⊴ R such that E(2l,R,A) ≤ H and, moreover, H normalizes EO(2l,R)E(2l,R,A). In the case where R = K is a field, similar results were obtained earlier by Dye, King, Li Shangzhi, and Bashkirov. Bibliography: 31 titles. [ABSTRACT FROM AUTHOR]

Let R be a commutative ring and G = GL(mn,R) the general linear group of degree mn over R. A wide class of overgroups of the elementary group Em(n,R), which is represented as the direct sum of m copies of the vector representation, is constructed and studied. If R = K is a field and n is large enough relative to m, this allows us to give a complete description of all subgroups intermediate between Em(n,R) and G. This is a very wide extension of some results of Z. I. Borevich, N. A. Vavilov, and others. Bibliography: 4 titles. [ABSTRACT FROM AUTHOR]

We describe the subgroups of the general linear group GL(n,R) over the field of fractions K of a local principal ideal domain R, containing the group SD(n,R) of diagonal matrices with entries from R and determinant 1. Similar results for overgroups of D(n,R) were obtained earlier by I. Hamdan and N. Vavilov. The results of the present paper generalize also some other known results, especially the description of parahoric subgroups by N. Iwahori and H. Matsumoto. Bibliography: 22 titles. [ABSTRACT FROM AUTHOR]

The subgroups generated by a long and a short root subgroup in a Chevalley group of type G2 are described, and the orbits of the group acting on such pairs by simultaneous conjugation are classified. Bibliography: 18 titles. [ABSTRACT FROM AUTHOR]

Discusses the conditions necessary for the equicontinuity of maps on figure-eight space. Substitutions on metric space; Theorems in the equicontinuous map; Information on quotient space sets in the mathematical setting.

When a fixed algebraic variety in a multiplicative group variety is intersected with the union of all algebraic subgroups of fixed dimension, a key role is played by what we call the anomalous subvarieties. These arise when the algebraic variety meets translates of subgroups in sets larger than expected. We prove a Structure Theorem for the anomalous subvarieties, and we give some applications, emphasizing in particular the case of codimension two. We also state some related conjectures about the boundedness of absolute height on such intersections as well as their finiteness. [ABSTRACT FROM PUBLISHER]