On strongly closed and Hall s-semiembedded subgroups of finite groups.

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.]. [ABSTRACT FROM AUTHOR]