Search

In this paper we investigate generalized Bernoulli and Euler polynomials. In section 1, we enter multiplication theorem for generalized Bernoulli and Euler numbers. Aslo in section 2, we introduce a matrix representation of [B.sup.-1.sub.n] and [E.sup.-1.sub.n] . Furthermore in section 3 we consider Euler Maclaurin summation formula for [alpha]- Bernoulli numbers and in section 4 we give a relation between associated stirling numbers and [B.sub.n](a, b). Also in end section of this paper we consider a new method for representation of Apostol Bernoulli numbers. Keywords Bernoulli numbers, Euler polynomials, Stirling numbers of the second kind, generating functions., Short review of classical approaches Bernoulli numbers were first introduced by Jacques Bernoulli (1654-1705), in the second part of his treatise published in 1713, Ars conjectandi , at the time, [...]

In this paper we determine all tetravalent Cayley graphs of a non-abelian group of order 3 p2, where p is a prime number greater than 3, and with a cyclic Sylow p-subgroup. We show that all of these tetravalent Cayley graphs are normal. The full automorphism group of these Cayley graphs is given and the half-transitivity and the arc-transitivity of these graphs are investigated. We show that this group is a 5-CI-group. [ABSTRACT FROM AUTHOR]

In this paper we determine all tetravalent Cayley graphs of a non-abelian group of order 3 p2, where p is a prime number greater than 3, and with a cyclic Sylow p-subgroup. We show that all of these tetravalent Cayley graphs are normal. The full automorphism group of these Cayley graphs is given and the half-transitivity and the arc-transitivity of these graphs are investigated. We show that this group is a 5-CI-group. [ABSTRACT FROM AUTHOR]

LetGa finite group. For conjugacy classesAandBofG, the subsetABofGis a union of conjugacy classes ofG, and for irreducible complex characters χ and ϕ ofG, the product χϕ is a linear combination of irreducible characters ofGwith positive integer coefficients. In this article we give the structure of finite groupsGwheneverC2contains a central conjugacy class or does not contain a central conjugacy class ofG, for all conjugacy classesCofG. Also in the case of (C−1)mCn ⊆ Z(G) the structure ofGis given. Similar results whenCis replaced by an irreducible character χ ofGare discussed. [ABSTRACT FROM AUTHOR]

The author will prove that the group 2 D p (3) can be uniquely determined by its order components, where p ≠ 2 m + 1 is a prime number, p ≥ 5. More precisely, if OC( G) denotes the set of order components of G, we will prove OC( G) = OC(2 D p (3)) if and only if G is isomorphic to 2 D p (3). A main consequence of our result is the validity of Thompson’s conjecture for the groups under consideration. [ABSTRACT FROM AUTHOR]

.A square matrix over the complex field with non-negative integral trace is called a quasi-permutation matrix. For a finite group G the minimal degree of a faithful permutation representation of G is denoted by p(G). The minimal degree of a faithful representation of G by quasi-permutation matrices over the rational and the complex numbers are denoted by q(G) and c(G) respectively. Finally r(G) denotes the minimal degree of a faithful rational valued complex character of G. In this paper p(G), q(G), c(G) and r(G) are calculated for the groups PSU(3,q[sup 2] ) and SU(3,q[sup 2] ). [ABSTRACT FROM AUTHOR]

Presents a study on symmetry classes of tensors associated with any finite group and its irreducible complex character. Formula for the dimension symmetry classes tensors; Discussion on the non-vanishing basis of symmetry; Condition for the existence of orthogonal basis of decomposable symmetrized tensors.