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

Let H <= K be subgroups of a finite group C, then H is called strongly closed in K with respect to G if H-g boolean AND K <= H for every g is an element of 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 is an element of Syl(p)(G), where (vertical bar H vertical bar, 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.].