Character codegrees of maximal class p-groups

2018/09/20 by Sarah Croome, Mark L. Lewis, Croome, Sarah +1 · 1 citation
Computer Science · Engineering · Mathematics · #20C15 #20D15 #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.1809.07699

openalex publication_date 2018/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a p-group and let χ be an irreducible character of G. The codegree of χ is given by |G:ker(χ)|/χ(1). If G is a maximal class p-group that is normally monomial or has at most three character degrees then the codegrees of G are consecutive powers of p. If |G|=pⁿ and G has consecutive p-power codegrees up to p^n-1 then the nilpotence class of G is at most 2 or G has maximal class.

Cited by

• p-groups with exactly four codegrees

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• p-groups with exactly four codegrees
• Two results on character codegrees
• p-groups with p² as a codegree
• Finite groups in which every irreducible character has either p'-degree or p'-codegree
• Character degrees of some p-groups