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 group...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.展开更多
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 ...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.展开更多
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 pro...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.展开更多
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 sub...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.展开更多
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 su...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.展开更多
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...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.展开更多
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...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.展开更多
文摘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.
基金Supported by the Natural Science Foundation of Hubei Province( No.99J16 5 )
文摘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.
基金Supported by NSF of China(11171169)the B.S.Foundation of Shandong Province(BS2012SF003)
文摘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.
基金The author is supported in part by NSF of China and NSF of Guangdong Province
文摘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.
基金Supported by National Natural Science Foundation of China (Grant No.10871210)Natural Science Foundation of Guangdong Province (Grant No.06023728)
文摘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.
基金the National Natural Science Foundation of China(10471085)the Shanghai Pujiang Program(05PJ14046)the Special Funds for Major Specialities of Shanghai Education Committee
文摘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.
基金Supported by the National Natural Science Foundation of China (Grant No10871210)the Natural Science Foundation of Guangdong Province (Grant No06023728)
文摘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.