Finite p-groups All of Whose Minimal Nonabelian Subgroups are Nonmetacyclic of Order p^3  

作　　者：Qin Hai ZHANG 

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

出　　处：《Acta Mathematica Sinica,English Series》2019年第7期1179-1189,共11页数学学报（英文版）

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

摘　　要：Assume p is an odd prime. We investigate finite p-groups all of whose minimal nonabelian subgroups are of order p^3. Let P1-groups denote the p-groups all of whose minimal nonabelian subgroups are nonme tacyclic of order p^3. In this paper, the P1-groups are classified, and as a by-product, we prove the Hughes' conjecture is true for the P1-groups.Assume p is an odd prime. We investigate finite p-groups all of whose minimal nonabelian subgroups are of order p3. Let P1-groups denote the p-groups all of whose minimal nonabelian subgroups are nonmetacyclic of order p3. In this paper, the P1-groups are classified, and as a by-product,we prove the Hughes’ conjecture is true for the P1-groups.

关 键 词：Finite P-GROUPS a MINIMAL nonabelian SUBGROUP the HUGHES SUBGROUP P-GROUPS of MAXIMAL class 

分 类 号：O1[理学—数学]