On the sum of character codegrees of finite groups

2024/02/20 by Mark L. Lewis, Lewis, Mark L., Quanfu Yan +1
Computer Science · Engineering · Mathematics · #Coding theory and cryptography #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #graph theory and CDMA systems

paper · pdf · doi:10.48550/arxiv.2402.12628

openalex publication_date 2024/02/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let χ be an irreducible character of a group G. We denote the sum of the codegrees of the irreducible characters of G by S_c(G)=∑_χ∈ \rm Irr(G)\rm cod(χ). We consider the question if S_c(G)≤ S_c(C_n) is true for any finite group G, where n=|G| and C_n is a cyclic group of order n. We show this inequality holds for many classes of groups. In particular, we provide an affirmative answer for any finite group whose order is divisible by up to 99 primes. However, we show that the question does not hold true in all cases, by evidence of a counterexample.

Related

• A note on the codegree of finite groups
• On the multiplicities of the character codegrees
• Two results on character codegrees
• On the relation of character codegrees and the minimal faithful quasi-permutation representation degree of p-groups
• Finite groups in which every irreducible character has either p'-degree or p'-codegree