Finite groups with coprime non-linear codegrees
Ashkan Zarezadeh, Behrooz Khosravi, Zeinab Akhlaghi

TL;DR
This paper classifies finite groups where the set of non-linear irreducible character codegrees contains multiple elements that are pairwise coprime, revealing structural properties related to character theory.
Contribution
It provides a complete classification of finite groups with multiple coprime non-linear codegrees, a new insight in character theory of finite groups.
Findings
Identifies conditions for groups with coprime non-linear codegrees
Classifies all such finite groups
Establishes relationships between group structure and codegree properties
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.
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Taxonomy
TopicsFinite Group Theory Research · Coding theory and cryptography · Rings, Modules, and Algebras
