Groups with 2-generated Sylow subgroups and their character tables

Alexander Moretó and Benjamin Sambale

Vol. 323 (2023), No. 2, 337–358

DOI: 10.2140/pjm.2023.323.337

Abstract

Let $G$ be a finite group with a Sylow $p$-subgroup $P$. We show that the character table of $G$ determines whether $P$ has maximal nilpotency class and whether $P$ is a minimal nonabelian group. The latter result is obtained from a precise classification of the corresponding groups $G$ in terms of their composition factors. For $p$-constrained groups $G$ we prove further that the character table determines whether $P$ can be generated by two elements.

Keywords

maximal class, minimal nonabelian, Sylow subgroup, fusion system, character table

Mathematical Subject Classification

Primary: 20C15, 20D20

Milestones

Received: 7 September 2022

Revised: 15 April 2023

Accepted: 26 April 2023

Published: 2 June 2023