Groups with 2-generated Sylow subgroups and their character tables
Representation Theory
2023-06-07 v2 Group Theory
Abstract
Let G be a finite group with 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 non-abelian 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.
Cite
@article{arxiv.2205.13167,
title = {Groups with 2-generated Sylow subgroups and their character tables},
author = {Alexander Moretó and Benjamin Sambale},
journal= {arXiv preprint arXiv:2205.13167},
year = {2023}
}
Comments
Gunter's comments incorporated, 18 pages