Finite Groups Whose Some Subgroups Are S-seminormal

A subgroup H is called S-seminormal in a finite group G if H permutes with all Sylow p-subgroups of G with (p, |H| =1. The main object of this paper is to generalize some known results about finite supersolvable groups to a saturated formation containing the class of finite supersolvable groups.

The Structure of One Type of Non-Abelian Group

By the property of the solvable group and the extending theorem of group, the authors acquired the structure of one type of Non-Abelian group. And we proved that when order is 10p n (p#2,5) and the sylowp-subgroup is cyclic, the group has twenty types. Whenp#3, it has 12 types and whenp=3, it has 8 types.

ON COLEMAN OUTER AUTOMORPHISM GROUPS OF FINITE GROUPS

Let G be a finite group and Outcoz（G） the Coleman outer automorphism group of G（for the definition, see below）. The question whether Outcol（G） is a p′-group naturally arises from the study of the normalizer problem for integral group rings, where p is a prime. In this article, some sufficient conditions for OutCol（G） to be a p＇-group are obtained. Our results generalize some well-known theorems.

The Influence of Minimal Subgroups on the Structure of Finite Groups

Let G be a finite group.The question how the properties of its minimal subgroups influence the structure of G is of considerable interest for some scholars.In this paper we try to use c-normal condition on minimal subgroups to characterize the structure of G.Some previously known results are generalized.

On s-semipermutable Subgroups of Finite Groups

Suppose that G is a finite group and H is a subgroup of G. We say that H is ssemipermutable in G if HGv = GpH for any Sylow p-subgroup Gp of G with （p, ｜H｜） = 1. We investigate the influence of s-semipermutable subgroups on the structure of finite groups. Some recent results are generalized and unified.

On Finite Groups with Some Semi Cover-Avoiding Subgroups

A subgroup H of a finite group G is said to have the semi-cover-avoiding property in G if there is a chief series of G such that H covers or avoids every chief factor of the series. In this paper, some new results are obtained based on the assumption that some subgroups have the semi-cover-avoiding property in the group.

On X-s-Permutable Subgroups of a Finite Group

Let X be a nonempty subset of a group G. A subgroup H of G is said to be X- s-permutable in G if there exists an element x E X such that HP^x = P^xH for every Sylow subgroup P of G. In this paper, some new results are given under the assumption that some suited subgroups of G are X-s-permutable in G.