On the Multiplicities of the Character Codegrees of Finite Groups

Abstract

Let G be a finite group and χ be an irreducible character of G, the number cod (χ) = | G: ker(χ) | / χ(1 ) is called the codegree of χ. Also, cod(G) = {cod(χ) | χ ∈Irr(G)}. For d ∈cod(G), the multiplicity of d in G, denoted by mG′(d), is the number of irreducible characters of G having codegree d. A finite group G is called a Tk′-group for some integer k ≥ 1, if there exists d0 ∈cod(G) such that mG′(d0)=k and for every d ∈cod(G) −{d0}, we have mG′(d)=1. In this note we characterize finite Tk′-groups completely, where k ≥ 1 is an integer. © 2022, The Author(s), under exclusive licence to Springer Nature B.V.