Let E/F be a Galois extension of number fields with Galois group G. The purpose of this paper is to place limitations on the structure of a Sylow 2-subgroup of G in the case when the extension E/F is a minimal counterexample to Artin’s Conjecture on the holomorphy of L-series. More specifically, assume for some s0 ∈ C − {1} and some irreducible character χ of G that the Artin L-series L(s, χ,E/...

Clifford theory of finite groups is generalized to association schemes. It shows a relation between irreducible complex characters of a scheme and a strongly normal closed subset of the scheme. The restriction of an irreducible character of a scheme to a strongly normal closed subset coniatns conjugate characters with same multiplicities. Moreover some strong relations are obtained.

‎Let $G$ be a finite group‎. ‎An element $gin G$ is called non-vanishing‎, ‎if for‎ ‎every irreducible complex character $chi$ of $G$‎, ‎$chi(g)neq 0$‎. ‎The bi-Cayley graph ${rm BCay}(G,T)$ of $G$ with respect to a subset $Tsubseteq G$‎, ‎is an undirected graph with‎ ‎vertex set $Gtimes{1,2}$ and edge set ${{(x,1),(tx,2)}mid xin G‎, ‎ tin T}$‎. ‎Let ${rm nv}(G)$ be the set‎ ‎of all non-vanishi...

A finite group G is odd-square-free if no irreducible complex character of G has degree divisible by the square of an odd prime. We determine all odd-square-free groups G satisfying S 6 G 6 Aut(S) for a finite simple group S. More generally, we show that ifG is any nonsolvable odd-square-free group, then G has at most two nonabelian chief factors and these must be simple odd-square-free groups....

A Brauer character of a finite group may be lifted to an ordinary character if it lies in a block whose defect groups are contained in a normal p-solvable subgroup. By the Fong-Swan theorem [2, Theorem 72.1], an irreducible Brauer character of a finite p-solvable group G may be lifted to an ordinary (complex) character of G. In other words, every Brauer character is the restriction of some ...

By a quasi-permutation matrix we mean a square matrix over the complex field C with non-negative integral trace. Thus every permutation matrix over C is a quasipermutation matrix. For a given finite group G, let p(G) denote the minimal degree of a faithful permutation representation of G (or of a faithful representation of G by permutation matrices), let q(G) denote the minimal degree of a fai...

An explicit character formula is established for any strongly generic finite-dimensional irreducible g-module, g being an arbitrary finite-dimensional complex Lie superalgebra. This character formula had been conjectured earlier by Vera Serganova and the author for any generic irreducible finite-dimensional g-module, i.e. such that its highest weight is far enough from the walls of the Weyl cha...

An explicit character formula is established for any strongly generic nite-dimensional irreducible g-module, g being an arbitrary nite-dimensional complex Lie superalgebra. This character formula had been conjectured earlier by Vera Serganova and the author for any generic irreducible nite-dimensional g-module, i.e. such that its highest weight is far enough from the walls of the Weyl chambers....

the aim of this paper is to classify the finite simple groups with the number of zeros at most seven greater than the number of nonlinear irreducible characters in the character tables. we find that they are exactly a$_{5}$, l$_{2}(7)$ and a$_{6}$.

‎Let $G$ be a finite group‎. ‎We say that an element $g$ in $G$ is a vanishing element if there exists some irreducible character $chi$ of $G$ such that $chi(g)=0$‎. ‎In this paper‎, ‎we classify groups whose set of vanishing elements is exactly a conjugacy class‎.