ON WEAKLY SS-QUASINORMAL AND HYPERCYCLICALLY EMBEDDED PROPERTIES OF FINITE GROUPS

A subgroup h is said to be s-permutable in a group g, if hp = ph holds for every sylowsubgroup p of g. if there exists a subgroup b of g such that hb = g and h permutes with every sylowsubgroup of b, then h is said to be ss-quasinormal in g. in this paper, we say that h is a weaklyss-quasinormal subgroup of g, if there is a normal subgroup t of g such that ht is s-permutableand h t is ss-quasinormal in g. by assuming that some subgroups of g with prime power orderhave the weakly ss-quasinormal properties, we get some new characterizations about the hypercyclicallyembedded subgroups of g. a series of known results in the literature are unified and generalized.