$s$-Conditionally Permutable Subgroups and $p$-Nilpotency of Finite Groups

Abstract

We study the $p$-nilpotency of a group such that every maximal subgroup of its Sylow $p$-subgroups is $s$-conditionally permutable for some prime $p$. By using the classification of finite simple groups, we get interesting new results and generalize some earlier results.