A subgroup H of finite group G is called pronormal in G if for every element x of G, H is conjugate to Hx in (H, Hx). A finite group G is called PRN-group if every cyclic subgroup of G of prime order or order 4 is p...A subgroup H of finite group G is called pronormal in G if for every element x of G, H is conjugate to Hx in (H, Hx). A finite group G is called PRN-group if every cyclic subgroup of G of prime order or order 4 is pronormal in G. In this paper, we find all PRN-groups and classify minimal non-PRN-groups (non-PRN-group all of whose proper subgroups are PRN-groups). At the end of the paper, we also classify the finite group G, all of whose second maximal subgroups are PRN-groups.展开更多
In this paper, we study finite groups all of whose nontrivial normal subgroups have the same order. In the solvable case, the groups are determined. In the insolvable case, some characterizations are given.
基金Supported by Natural Science Foundation of China (Grant No. 10871032), Graduate Student Research and Innovation Program of Jiangsu Province (Grant No. CX10B-028Z)
文摘A subgroup H of finite group G is called pronormal in G if for every element x of G, H is conjugate to Hx in (H, Hx). A finite group G is called PRN-group if every cyclic subgroup of G of prime order or order 4 is pronormal in G. In this paper, we find all PRN-groups and classify minimal non-PRN-groups (non-PRN-group all of whose proper subgroups are PRN-groups). At the end of the paper, we also classify the finite group G, all of whose second maximal subgroups are PRN-groups.
基金the National Natural Science Foundation of China (No.10671114)the Natural Science Foun-dation of Shanxi Province (No.20051007)the Returned Abroad-student Fund of Shanxi Province (No.[2004]13-56)
文摘In this paper, we study finite groups all of whose nontrivial normal subgroups have the same order. In the solvable case, the groups are determined. In the insolvable case, some characterizations are given.
基金Supported by National Natural Science Foundation of China(11661031)Jiangsu Overseas Research&Training Program for University Prominent Young & Middle-Aged Teachers and Presidents+1 种基金"333" Project of Jiangsu Province(BRA2015137)"521" Project of Lianyungang City