Finite groups with coprime non-linear codegrees
Group Theory
2024-12-19 v1
Abstract
Given a finite group G with an irreducible character \chi \in Irr(G), the codegree of \chi is defined by cod(\chi) = |G :\ker \chi|/\chi(1). The set of non-linear irreducible character codegrees of G is denoted by cod(G|G'). In this note, we classify all finite groups G with |cod(G|G')|> 1 and for each pair of distinct elements m, n \in cod(G|G'), m and n are coprime.
Cite
@article{arxiv.2412.13926,
title = {Finite groups with coprime non-linear codegrees},
author = {Ashkan Zarezadeh and Behrooz Khosravi and Zeinab Akhlaghi},
journal= {arXiv preprint arXiv:2412.13926},
year = {2024}
}