ON WEAKLY -PERMUTABLY EMBEDDED SUBGROUPS OF FINITE GROUPS

Abstract

In this paper, we obtain some criteria for $p$-nilpotency and $p$-supersolvability of a finite group and extend some known results concerning weakly $S$-permutably embedded subgroups. In particular, we generalise the main results of Zhang et al. [‘Sylow normalizers and $p$-nilpotence of finite groups’, Comm. Algebra43(3) (2015), 1354–1363].