A Classification of Finite Metahamiltonian p-Groups  

作　　者：Xingui Fang Lijian An 

机构地区：[1]School of Mathematics Science,Peking University,Beijing 100087,People’s Republic of China [2]Department of Mathematics,Shanxi Normal University,Linfen 041004,Shanxi,People’s Republic of China

出　　处：《Communications in Mathematics and Statistics》2021年第2期239-260,共22页数学与统计通讯（英文）

基　　金：This work was supported by NSFC(Nos.11971280,11771258).

摘　　要：A finite non-abelian group G is called metahamiltonian if every subgroup of G is either abelian or normal in G.If G is non-nilpotent,then the structure of G has been determined.If G is nilpotent,then the structure of G is determined by the structure of its Sylow subgroups.However,the classification of finite metahamiltonian p-groups is an unsolved problem.In this paper,finite metahamiltonian p-groups are completely classified up to isomorphism.

关 键 词：Minimal non-abelian groups Hamiltonian groups Metahamiltonian groups A_(2)-groups 

分 类 号：O15[理学—数学]