Finite groups with real-valued irreducible characters of prime degree

Abstract

In this paper we describe the structure of finite groups whose real-valued nonlinear irreducible characters have all prime degree. The more general situation in which the real-valued irreducible characters of a finite group have all squarefree degree is also considered.A classical problem in Character Theory is understanding to what extent the set cd(G) of (distinct) degrees of the irreducible characters of a finite group G determines the structure of G.Here we consider the subset cd rv (G) of cd(G) whose elements are the degrees of the realvalued irreducible characters of G. In particular, we consider the case when cd rv (G)\{1} consists of prime numbers.

On the character tables of symmetric groups

“…Also, it seems that there is no a simple way to construct them. However, many researchers devoted times to study some general behavior of character tables, see for example [1,2,3,5,11,13].…”