A finite group G is called a generalized PST-group if every subgroup contained in F（G） permutes all Sylow subgroups of G, where F（G） is the Fitting subgroup of G. The class of generalized PST-groups is not subgrou...A finite group G is called a generalized PST-group if every subgroup contained in F（G） permutes all Sylow subgroups of G, where F（G） is the Fitting subgroup of G. The class of generalized PST-groups is not subgroup and quotient group closed, and it properly contains the class of PST-groups. In this paper, the structure of generalized PST-groups is first investigated. Then, with its help, groups whose every subgroup （or every quotient group） is a generalized PST-group are deter- mined, and it is shown that such groups are precisely PST-groups. As applications, T-groups and PT-groups are characterized.展开更多
Letσ={σi|i∈I}be some partition of the set P of all primes and G afinite group.A set H of subgroups of G is said to be a complete Hallσ-set of G ifevery member≠1 of H is a Hallσi-subgroup of G for some i c l and ...Letσ={σi|i∈I}be some partition of the set P of all primes and G afinite group.A set H of subgroups of G is said to be a complete Hallσ-set of G ifevery member≠1 of H is a Hallσi-subgroup of G for some i c l and H containsexactly one Hallσi-subgroup of G for every i such thatσi∩π(G)≠Ø.A subgroupA of G is said to be H-permutable if A permutes with all members of the completeHallσ-set H of G.In this paper,we study the structure of G under the assuming thatsome subgroups of G areσ-permutable.展开更多
基金The NSF(11071155)of Chinathe Science and Technology Foundation (20081022)of Shanxi Province for Collegesthe Team Innovation Research Foundation of Shanxi University of Finance andEconomics
文摘A finite group G is called a generalized PST-group if every subgroup contained in F（G） permutes all Sylow subgroups of G, where F（G） is the Fitting subgroup of G. The class of generalized PST-groups is not subgroup and quotient group closed, and it properly contains the class of PST-groups. In this paper, the structure of generalized PST-groups is first investigated. Then, with its help, groups whose every subgroup （or every quotient group） is a generalized PST-group are deter- mined, and it is shown that such groups are precisely PST-groups. As applications, T-groups and PT-groups are characterized.
基金a NNSF grant of China(Grant#11371335)Wu Wen-TsunKey Laboratory of Mathematics of Chinese Academy of Sciences.Research of the third author is supported by Chinese Academy of Sciences Visiting Professorship for Senior International Scientists(Grant No.2010T2J12).
文摘Letσ={σi|i∈I}be some partition of the set P of all primes and G afinite group.A set H of subgroups of G is said to be a complete Hallσ-set of G ifevery member≠1 of H is a Hallσi-subgroup of G for some i c l and H containsexactly one Hallσi-subgroup of G for every i such thatσi∩π(G)≠Ø.A subgroupA of G is said to be H-permutable if A permutes with all members of the completeHallσ-set H of G.In this paper,we study the structure of G under the assuming thatsome subgroups of G areσ-permutable.
