相关论文: Zeros of primitive characters of finite groups

We prove certain polynomial relations between the values of complex irreducible characters of general finite symmetric groups. We use it to find some sets of conjugacy classes such that no finite symmetric group has a complex irreducible…

We investigate a beautiful conjecture of T. Wilde on character values and element orders of finite groups. We reduce it to a statement on nearly simple groups that can be checked ``prime by prime". For these groups, we show that a strong…

Let $G$ be a finite group, and let $\text{Irr}(G)$ denote the set of the irreducible complex characters of $G$. An element $g\in G$ is called a vanishing element of $G$ if there exists $\chi\in\text{Irr}(G)$ such that $\chi(g)=0$ (i.e., $g$…

The concept of $S$-characters of finite groups was introduced by Zhmud' as a generalisation of transitive permutation characters. Any non-trivial $S$-character takes a zero value on some group element. By a deep result depending on the…

Let X be an irreducible, primitive complex character of the finite solvable group G, and let X* denote the complex conjugate character. If the degree X(1) is odd, then we show how to associate to X in a unique way, a conjugacy class of…

We obtain the codegree of a certain primitive character for a finite solvable group, and thereby give a negative answer to a question proposed by Moret\'o in \cite{Moreto}.

A classical theorem on character degrees states that if a finite group has fewer than four character degrees, then the group is solvable. We prove a corresponding result on character values by showing that if a finite group has fewer than…

In representation theory of finite groups an important role is played by irreducible characters of p-defect 0, for a prime p dividing the group order. These are exactly those vanishing at the p-singular elements. In this paper we generalize…

Let $G$ be a finite group of odd order. We show that if $\chi$ is an irreducible primitive character of $G$ then for all primes $p$ dividing the order of $G$ there is a conjugacy class such that the $p-$part of $\chi(1)$ divides the size of…

Let $ G $ be a finite non-solvable group with a primitive irreducible character $ \chi $ that vanishes on one conjugacy class. We show that $ G $ has a homomorphic image that is either almost simple or a Frobenius group. We also classify…

We prove a broad generalization of a theorem of W. Burnside on real characters using permutation characters. Under a necessary hypothesis, We can give some control on multiplicities (a result that needs the Classification of Finite Simple…

Building upon the author's previous work on primitivity testing of finite nilpotent linear groups over fields of characteristic zero, we describe precisely those finite nilpotent groups which arise as primitive linear groups over a given…

We study the zero-sharing behavior among irreducible characters of a finite group. For symmetric groups $S_n$, it is proved that, with one exception, any two irreducible characters have at least one common zero. To further explore this…

An element $g$ of a finite group $G$ is said to be vanishing in $G$ if there exists an irreducible character $\chi$ of $G$ such that $\chi(g)=0$; in this case, $g$ is also called a zero of $G$. The aim of this paper is to obtain structural…

The aim of this paper is to classify the finite nonsolvable groups in which every irreducible character of even degree vanishes on at most two conjugacy classes. As a corollary, it is shown that $L_2(2^f)$ are the only nonsolvable groups in…

We classify the finite groups $G$ which satisfies the condition that every complex irreducible character,whose degree's square doesn't divide the index of its kernel in $G$, lies in the same Galois conjugacy class.

The concept of a supercharacter theory of a finite group was introduced by Diaconis and Isaacs as an alternative to the usual irreducible character theory, and exemplified with a particular construction in the case of finite algebra groups.…

In this article we extend independent results of Lusztig and H\'ezard concerning the existence of irreducible characters of finite reductive groups, (defined in good characteristic and arising from simple algebraic groups), satisfying a…

A complex irreducible character of a finite group G is said to be p-constant, for some prime p dividing the order of G, if it takes constant value at the set of p-singular elements of G. In this paper we classify irreducible p-constant…

Motivated by the Problem $164$ proposed by Y. Berkovich and E. Zhmud' in their book "Characters of finite groups, Part $1$", we give a characterization of finite groups whose irreducible character codegrees are prime powers. This is based…