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
Let H be a subgroup of a group G. Then H is said to be S-quasinormal in G if HP = PH for every Sylow subgroup P of G; H is said to be S-quasinormally embedded in G if a Sylow p-subgroup of H is also a Sylow p-subgroup...Let H be a subgroup of a group G. Then H is said to be S-quasinormal in G if HP = PH for every Sylow subgroup P of G; H is said to be S-quasinormally embedded in G if a Sylow p-subgroup of H is also a Sylow p-subgroup of some S-quasinormal subgroup of G for each prime p dividing the order of H. In this paper, we say that H is weakly S-embedded in G if G has a normal subgroup T such that HT is an S-quasinormal subgroup of G and H VIT ≤ HSE, where HSE denotes the subgroup of H generated by all those subgroups of H which are S-quasinormally embedded in G. Some results about the influence of weakly S-embedded subgroups on the structure of finite groups are given.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
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supported by National Natural Science Foundation of China (Grant Nos.10771172,11001226)Postgraduate Innovation Foundation of Southwest University (Grant Nos. ky2009013,ky2010007)
文摘Let H be a subgroup of a group G. Then H is said to be S-quasinormal in G if HP = PH for every Sylow subgroup P of G; H is said to be S-quasinormally embedded in G if a Sylow p-subgroup of H is also a Sylow p-subgroup of some S-quasinormal subgroup of G for each prime p dividing the order of H. In this paper, we say that H is weakly S-embedded in G if G has a normal subgroup T such that HT is an S-quasinormal subgroup of G and H VIT ≤ HSE, where HSE denotes the subgroup of H generated by all those subgroups of H which are S-quasinormally embedded in G. Some results about the influence of weakly S-embedded subgroups on the structure of finite groups are given.
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.
