SS-QUASINORMAL SUBGROUPS OF FINITE GROUPS.

A subgroup H of a finite group G is said to be SS-quasinormal in G if there exists a supplement B of H in G such that H is permutable with every Sylow subgroup of B. In this paper, we get some new characterizations of supersolvability and p-nilpotency of G by assuming some subgroups of prime power order of G are SS-quasinormal. [ABSTRACT FROM AUTHOR]