p-groups with exactly four codegrees

2019/01/22 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 #math.GR #msc:20C15 #msc:20D15

paper · pdf · doi:10.48550/arxiv.1901.07425

arxiv created 2019/01/22 · openalex publication_date 2019/01/22 · arxiv updated 2019/01/23 · 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). Du and Lewis have shown that a p-group with exactly three codegrees has nilpotence class at most 2. Here we investigate p-groups with exactly four codegrees. If, in addition to having exactly four codegrees, G has two irreducible character degrees, G has largest irreducible character degree p², |G:G'|=p², or G has coclass at most 3, then G has nilpotence class at most 4. In the case of coclass at most 3, the order of G is bounded by p⁷. With an additional hypothesis we can extend this result to p-groups with four codegrees and coclass at most 7. In this case the order of G is bounded by p¹¹.

Citations

• Character codegrees of maximal class p-groups

Cited by

• Finite groups of non-prime-power order with exactly four character codegrees

Related

• p-groups with p² as a codegree
• Character codegrees of maximal class p-groups
• Finite groups of non-prime-power order with exactly four character codegrees
• Finite groups in which every irreducible character has either p'-degree or p'-codegree
• Two results on character codegrees