Finite p-groups whose nonnormal subgroups are metacyclic  

作　　者：Qiangwei Song Haipeng Qu 

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

出　　处：《Science China Mathematics》2020年第7期1271-1284,共14页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant Nos.11771258 and 11471198)。

摘　　要：For an odd prime p,we give a criterion for finite p-groups whose nonnormal subgroups are metacyclic,and based on the criterion,the p-groups whose nonnormal subgroups are metacyclic are classified up to isomorphism.This solves a problem proposed by Berkovich.

关 键 词：metacyclic groups minimal nonabelian groups minimal nonmetacyclic groups p-groups of maximal class the rank of a p-group 

分 类 号：O152.1[理学—数学]