Finite p-groups whose non-normal subgroups have few orders  

作　　者：Lijian AN 

机构地区：[1]Department of Mathematics, Shanxi Normal University, Linfen 041004, China

出　　处：《Frontiers of Mathematics in China》2018年第4期763-777,共15页中国高等学校学术文摘·数学（英文）

基　　金：This work was supported in part by the National Natural Science Foundation of China （Grant Nos. 11471198, 11771258）.

摘　　要：Suppose that G is a finite p-group. If G is not a Dedekind group, then G has a non-normal subgroup. We use p^M（G） and p^m（G） to denote the maximum and minimum of the orders of the non-normal subgroups of G, respectively. In this paper, we classify groups G such that M（G） 〈 2m（G） ^- 1. As a by-product, we also classify p-groups whose orders of non-normal subgroups are p^k and p^k＋1.Suppose that G is a finite p-group. If G is not a Dedekind group, then G has a non-normal subgroup. We use p^M（G） and p^m（G） to denote the maximum and minimum of the orders of the non-normal subgroups of G, respectively. In this paper, we classify groups G such that M（G） 〈 2m（G） ^- 1. As a by-product, we also classify p-groups whose orders of non-normal subgroups are p^k and p^k＋1.

关 键 词：Finite p-groups meta-hamiltonian p-groups non-normal subgroups 

分 类 号：O156.2[理学—数学] S852.4[理学—基础数学]