Finite p-groups All of Whose Minimal Nonabelian Subgroups are Nonmetacyclic of Order p3

被引：6

作者：

Zhang, Qin Hai ^{[1
]}

机构：

[1] Shanxi Normal Univ, Dept Math, Linfen 041004, Peoples R China

来源：

ACTA MATHEMATICA SINICA-ENGLISH SERIES | 2019年 / 35卷 / 07期

基金：

中国国家自然科学基金;

关键词：

Finite p-groups; a minimal nonabelian subgroup; the Hughes subgroup; p-groups of maximal class;

D O I：

10.1007/s10114-019-7308-x

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

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 nonmetacyclic 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.

引用

页码：1179 / 1189

页数：11

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