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- Title
On strongly closed and Hall s-semiembedded subgroups of finite groups.
- Authors
Yu, Haoran; Xu, Xiaowei; Zhang, Guanghao
- Abstract
Let H ≤ K be subgroups of a finite group G , then H is called strongly closed in K with respect to G if H g ∩ K ≤ H for every g ∈ G , and in particular, H is simply called strongly closed in G if H is strongly closed in N G (H) with respect to G. Let H be a subgroup of a finite group G , then H is called Hall s -semiembedded in G if H is a Hall subgroup of 〈 H , P 〉 for every P ∈ Syl p (G) , where (| H | , p) = 1. In this paper, we obtain some criteria for p -nilpotency of a finite group and extend some known results concerning strongly closed and Hall s -semiembedded subgroups. In particular, we generalize some main results of Guo and Li [Hall s -semiembedded subgroups and p -nilpotency of finite groups, Southeast Asian Bull. Math. 42(3) (2018) 367–374] and Kong [New characterizations of p -nilpotency of finite groups, J. Algebra Appl. 20(11) (2021) Article ID: 2150215, 6 pp.].
- Subjects
FINITE groups; SUBGROUP growth; ALGEBRA
- Publication
Journal of Algebra & Its Applications, 2023, Vol 22, Issue 9, p1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498823502018