Conjugacy classes of maximal cyclic subgroups and nilpotence class of p-groups

2022/01/14 by M. Bianchi, Bianchi, M., R. D. Camina +3
Mathematics · #20D15 #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Limits and Structures in Graph Theory

paper · pdf · doi:10.48550/arxiv.2201.05642

openalex publication_date 2022/01/14 · openalex created_date 2022/04/03 · openalex updated_date 2026/07/28

Abstract

In this paper, we set η(G) to be the number of conjugacy classes of maximal cyclic subgroups of G. We prove that if G is a p-group of order pⁿ and nilpotence class l, then η(G) is bounded below by a linear function in n/l.

Related

• Conjugacy classes of maximal cyclic subgroups
• Conjugacy classes of maximal cyclic subgroups of metacyclic p-groups
• On p-groups of maximal class
• On groups where the twisted conjugacy class of the unit element is a subgroup
• Multiplicities of conjugacy class sizes of finite groups