ON F-QUASINORMAL PRIMARY SUBGROUPS OF FINITE GROUPS

Let G be a finite group and F a formation. A subgroup H is called F-quasinormal in G if there exists a quasinormal subgroup T of G such that HT is quasinormal in G and (HnT)H(G)/H(G) is contained in the F-hypercenter Z(infinity)(F) (G/H(G)) of G/H(G). In this article, we study the structure of finite groups by using F-quasinormal subgroups and prove that: Let F be a saturated formation containing U and G be a group with a normal subgroup H such that G/H is an element of F. If every maximal subgroup of every noncyclic Sylow subgroup of F*(H) having no supersolvable supplement in G is U-quasinormal in G, then G is an element of F.