On the maximal overgroups of Sylow subgroups of finite groups

Barbara Baumeister; Tim  Burness; Robert Guralnick; Hung Tong-Viet

doi:10.48550/arXiv.2307.13976

On the maximal overgroups of Sylow subgroups of finite groups

Barbara Baumeister^*, Tim Burness^*, Robert Guralnick^*, Hung Tong-Viet^*

^*Corresponding author for this work

Research output: Contribution to journal › Article (Academic Journal) › peer-review

6 Citations (Scopus)

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.

Original language	English
Article number	109632
Number of pages	50
Journal	Advances in Mathematics
Volume	444
DOIs	https://doi.org/10.48550/arXiv.2307.13976 https://doi.org/10.1016/j.aim.2024.109632
Publication status	Published - 9 Apr 2024

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AU - Guralnick, Robert

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AB - 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.

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DO - 10.48550/arXiv.2307.13976

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VL - 444

JO - Advances in Mathematics

JF - Advances in Mathematics

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On the maximal overgroups of Sylow subgroups of finite groups

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