Related papers: Character formula for conjugacy classes in a coset

Let $H$ be an extension of a finite group $Q$ by a finite group $G$. Inspired by the results of duality theorems for \'etale gerbes on orbifolds, we describe the number of conjugacy classes of $H$ that maps to the same conjugacy class of…

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.

We provide an example of a finite group with a conjugacy class of average size on which fewer than half of the irreducible characters are either zero or a root of unity.

Much work has been done to study groups with few rational conjugacy classes or few rational irreducible characters. In this paper we look at the opposite extreme. Let $G$ be a finite group. Given a conjugacy class $K$ of $G$, we say it is…

Let $N$ be a normal subgroup of a finite group $G$. From a result due to Brauer, it can be derived that the character table of $G$ contains square submatrices which are induced by the $G$-conjugacy classes of elements in $N$ and the…

Let $G$ be a finite group and $A$, $B$ and $D$ be conjugacy classes of $ G$ with $D\subseteq AB=\{xy\mid x\in A, y\in B\}$. Denote by $\eta(AB)$ the number of distinct conjugacy classes such that $AB$ is the union of those. Set ${\bf…

In this paper, we compute the conjugacy classes and the list of irreducible characters of GSp(4,q), where q is odd. We also determine precisely which irreducible characters are non-cuspidal and which are generic. These characters are then…

If $G$ is a finite group, an irreducible complex-valued character $\chi$ is called rational if $\chi(g)$ is rational for all $g\in G$. Also, a conjugacy class $x^G$ is called rational, if for all irreducible complex-valued character $\chi$,…

Let $G$ be a finite group, $N$ a normal subgroup of $G$ and $x\in G-N$. We discuss when the coset $Nx$ is contained in the union of two conjugacy classes, $K$ and $D$, of $G$. We show that $N$ need not be solvable, and can even be…

Let $G$ be a finite group and let $\rm{Irr}(G)$ be the set of all irreducible complex characters of $G$. For a character $\chi \in \rm{Irr}(G)$, the number $\rm{cod}(\chi):=|G:\rm{ker}\chi|/\chi(1)$ is called the co-degree of $\chi$. The…

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., $g$…

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…

A group is nested if the centers of the irreducible characters form a chain. In this paper, we will show that there is a set of subgroups associated with the conjugacy classes of group so that a group is nested if and only if these…

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 N be a normal subgroup of a finite group G and consider the set cd(G|N) of degrees of irreducible characters of G whose kernels do not contain N. A number of theorems are proved relating the set cd(G|N) to the structure of N. For…

A special type of conjugacy classes in symmetric groups is studied and used to answer a question about odd-degree irreducible characters

Let G be a finite group and H a normal subgroup such that G/H is cyclic. Given a conjugacy class g^G of G we define its centralizing subgroup to be HC_G(g). Let K be such that H\le K\le G. We show that the G-conjugacy classes contained in K…

Let $G$ be a finite group. K. Harada conjectured that the product of degrees of all irreducible characters of $G$ divides the product of lengths of all conjugacy classes of $G$. We verify this conjecture for finite general linear groups and…

We compute conjugacy classes in maximal parabolic subgroups of the general linear group. This computation proceeds by reducing to a ``matrix problem''. Such problems involve finding normal forms for matrices under a specified set of row and…

A conjugacy class $C$ of a finite group $G$ is a sign conjugacy class if every irreducible character of $G$ takes value 0, 1 or -1 on $C$. In this paper we classify the sign conjugacy classes of alternating groups.