On $$s$$ s -semipermutable or ss-quasinormal subgroups of finite groups

Abstract

= 1; H is said to be an ss-quasinormal subgroup of G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B. We will study finite groups G saisfying the following: for each noncyclic Sylow subgroup P of G, there exists a subgroup D of P such that 1 < |D| < |P| and every subgroup H of P with order |D| is s-semipermutable or ss-quasinormal in G. Some recent results are generalized and unified.