Weakly subnormal subgroups and variations of the Baer-Suzuki theorem

2024/02/01 by Guralnick, Robert M., Tong-Viet, Hung P., Tracey, Gareth · 1 citation
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2402.00804

Abstract

A subgroup R of a finite group G is weakly subnormal in G if R is not subnormal in G but it is subnormal in every proper overgroup of R in G. In this paper, we first classify all finite groups G which contains a weakly subnormal p-subgroup for some prime p. We then determine all finite groups containing a cyclic weakly subnormal p-subgroup. As applications, we prove a number of variations of the Baer-Suzuki theorem using the orders of certain group elements.

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• Orders of commutators and Products of conjugacy classes in finite groups

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