Weakly subnormal subgroups and variations of the Baer-Suzuki theorem
arxiv(2024)
摘要
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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