On groups having a 𝑝-constant character

Dolfi, Silvio; Pacifici, Emanuele; Sanus, Lucía

doi:10.1090/proc/15256

On groups having a $p$-constant character
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by Silvio Dolfi, Emanuele Pacifici and Lucía Sanus PDF

Proc. Amer. Math. Soc. 149 (2021), 107-120 Request permission

Abstract:

Let $G$ be a finite group, and $p$ a prime number; a character of $G$ is called $p$-constant if it takes a constant value on all the elements of $G$ whose order is divisible by $p$. This is a generalization of the very important concept of characters of $p$-defect zero. In this paper, we characterize the finite $p$-solvable groups having a faithful irreducible character that is $p$-constant and not of $p$-defect zero, and we will show that a non-$p$-solvable group with this property is an almost-simple group.

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