一些特殊子群是TI-子群或次正规子群的有限群

Finite group in which some special subgroups are TI-subgroups or a subnormal subgroups

通过假设G的某些特殊子群是TI-子群或次正规子群来研究群G的结构.在研究过程中应用极小阶反例法等方法证明了:如果有限群G的每个非亚循环子群是TI-子群或次正规子群当且仅当G的每个非亚循环子群是次正规子群并且G可解.进一步应用分类讨论法等方法证明了:如果有限群G的每个自中心化子群是TI-子群或次正规子群或p-幂零子群,其中p为素数,则G的每个子群是次正规子群或p-可解子群.同时证明了如果有限群G的每个自中心化子群是TI-子群或次正规子群或p-幂零子群,则G的每个自中心化子群是正规子群或p-可解子群.

In this paper,we study the structure of groups G by assuming that some special subgroups are TI subgroups or subnormal subgroups.In the process of research,the minimum order counterexample method is used to prove that if the finite group if every non-metacyclic subg roup of a finite group G is a TI-subgroup or a subnormal subgroup of G if and only if every non-metacyclic subgroup of G must be subnormal subgroup and G is solvable.The classification discussion method is further applied to prove that if every self-centralizing subgroup of a finite group G is a TI-subgroup or a subnormal subgroup or a non-p-nilpotent subgroup of G,then every subgroup of G must be subnormal subgroup or p-solvable subgroup.It also proves that if every self-centralizing subgroup of a finite group G is a TI-subgroup or a subnormal subgroup or a non-p-nilpotent subgroup of G,then every self-centralizing subgroup of G must be subnormal subgroup or p-solvable subgroup.