On the maximal overgroups of Sylow subgroups of finite groups

Barbara Baumeister; Timothy C. Burness; Robert M. Guralnick; Hung P. Tong-Viet

On the maximal overgroups of Sylow subgroups of finite groups

Group Theory 2024-03-14 v2

Authors: Barbara Baumeister , Timothy C. Burness , Robert M. Guralnick , Hung P. Tong-Viet

Abstract

In this paper, we determine the finite groups with a Sylow $r$ -subgroup contained in a unique maximal subgroup. The proof involves a reduction to almost simple groups, and our main theorem extends earlier work of Aschbacher in the special case $r=2$ . Several applications are presented. This includes some new results on weakly subnormal subgroups of finite groups, which can be used to study variations of the Baer-Suzuki theorem.

Keywords

finite groups sylow subgroups maximal subgroups almost simple groups weakly subnormal subgroups baer-suzuki theorem

Cite

@article{arxiv.2307.13976,
  title  = {On the maximal overgroups of Sylow subgroups of finite groups},
  author = {Barbara Baumeister and Timothy C. Burness and Robert M. Guralnick and Hung P. Tong-Viet},
  journal= {arXiv preprint arXiv:2307.13976},
  year   = {2024}
}

Comments

50 pages; to appear in Advances in Mathematics

On the maximal overgroups of Sylow subgroups of finite groups

Abstract

Keywords

Cite

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