Finite groups with coprime non-linear codegrees

2024/12/18 by Zarezadeh, Ashkan, Khosravi, Behrooz, Akhlaghi, Zeinab
#05C25 #05C69 #94B25 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2412.13926

Abstract

Given a finite group G with an irreducible character χ∈ Irr(G), the codegree of χis defined by cod(χ) = |G :ker χ|/χ(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 ∈ cod(G|G'), m and n are coprime.

Related

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• Nonsolvable groups with three nonlinear irreducible character codegrees
• Finite groups with some bounded codegrees
• Finite groups of non-prime-power order with exactly four character codegrees
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