A note on the codegree of finite groups

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

paper · pdf · doi:10.48550/arxiv.2402.12632

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, and S_c(G)=∑_χ∈ \rm Irr(G)\rm cod(χ) be the sum of the codegrees of the irreducible characters of G. Write \rm fcod (G)=(S_c(G))/(|G|). We aim to explore the structure of finite groups in terms of \rm fcod (G). On the other hand, we determine the lower bound of S_c(G) for nonsolvable groups and prove that if G is nonsolvable, then S_c(G)≥ S_c(A₅)=68, with equality if and only if G≅ A₅. Additionally, we show that there is a solvable group so that it has the codegree sum as A₅.

Related

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