Search

Let G be a finite group and H a subgroup of G. We say that H has an IC-property if the intersection of H and [ H , G ] satisfy some conditions. In this paper, we investigate the structure of a finite group G under the assumption that some maximal subgroups, 2-maximal subgroups, 3-maximal subgroups of G have the ICp-property and obtain some new characterizations of p-solvable and solvable groups. [ABSTRACT FROM AUTHOR]

AbstractA subgroup S of a finite group G is called a p-sylowizer of a p-subgroup R in G if S is maximal in G with respect to having R as its Sylow p-subgroup. In this paper, we investigate pF -hypercentrally embedded structure of finite groups by using p-sylowizers of some p-subgroups with fixed order. [ABSTRACT FROM AUTHOR]

A subgroup H of a group G is called an ICΦs -subgroup of G if (H ∩ [ H , G ]) H G / H G ≤ Φ (H / H G) H s G / H G , where H G = ∩ g ∈ G H g and Φ (H / H G) is the Frattini subgroup of H / H G and HsG is the largest s-permutable subgroup of G contained in H. In this paper, we investigate the structure of finite group G under the assumption that some subgroups of G are ICΦs -subgroups of G, some results are obtained. [ABSTRACT FROM AUTHOR]