In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class J_(pr)is presented by establishing the r...In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class J_(pr)is presented by establishing the relationship between the core and the second maximal subgroups in these classifications.展开更多
This paper discusses the influence of minimal subgroups on the structure of finite groups and gives the structures of finite groups all of whose second maximal subgroups are PSC*-groups.
Let G be a finite group and assume that a group of automorphisms A is acting on G such that A and G have coprime orders.We prove that the fact of imposing specific properties on the second maximal A-invariant subgroup...Let G be a finite group and assume that a group of automorphisms A is acting on G such that A and G have coprime orders.We prove that the fact of imposing specific properties on the second maximal A-invariant subgroups of G determines that G is either soluble or isomorphic to a fewnon-soluble groups such as PSL(2,5)or SL(2,5).展开更多
In this paper, we investegate the intersection of a maximal intransitive subgroup with a maximal imprimitive subgroup. And, the structure of the second maximal intransitive subgroup of an alternating group is determined.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1237101812201236)+1 种基金the Fundamental Research Funds for the Central Universities(Grant No.B240201093/2013)the Natural Science Foundation of the Anhui Higher Education Institutions(Grant No.2022AH051907)。
文摘In this paper,we introduce the set of maximal subgroups with non-trivial core and their corresponding second maximal subgroups.A correlation characterization of the group class J_(pr)is presented by establishing the relationship between the core and the second maximal subgroups in these classifications.
基金the National Natural Science Foundation of China(No.10161001)Guangxi Autonomous Region(No.0249001)Innovation Project of Guangxi Graduate Education(No.2007105930701M30)
文摘This paper discusses the influence of minimal subgroups on the structure of finite groups and gives the structures of finite groups all of whose second maximal subgroups are PSC*-groups.
文摘Let G be a finite group and assume that a group of automorphisms A is acting on G such that A and G have coprime orders.We prove that the fact of imposing specific properties on the second maximal A-invariant subgroups of G determines that G is either soluble or isomorphic to a fewnon-soluble groups such as PSL(2,5)or SL(2,5).
文摘In this paper, we investegate the intersection of a maximal intransitive subgroup with a maximal imprimitive subgroup. And, the structure of the second maximal intransitive subgroup of an alternating group is determined.
