On the multiplicities of the character codegrees

2021/05/30 by Zeinab Akhlaghi, Akhlaghi, Zeinab, Mehdi Ebrahimi +3
Mathematics · Computer Science · Engineering · #Finite Group Theory Research #Coding theory and cryptography #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2105.14456

Abstract

Let G be a finite group and ? be an irreducible character of G, the number cod(?) = jG : Let G be a finite group and χ be an irreducible character of G , the number \cod(χ) = |G: \kernel(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 m'_G(d), is the number of irreducible characters of G having codegree d. A finite group G is called a T'_k-group for some integer k≥ 1, if there exists d₀∈\cod(G) such that m'_G(d₀)=k and for every d∈\cod(G)-\d₀\, we have m'_G(d)=1. In this note we characterize finite T'_k-groups completely, where k≥ 1 is an integer.

Related

• Two results on character codegrees
• Finite groups in which every irreducible character has either p'-degree or p'-codegree
• Finite groups with some bounded codegrees
• Finite groups of non-prime-power order with exactly four character codegrees
• On the sum of character codegrees of finite groups