Finite p-groups with a minimal non-abelian subgroup of index p (I)

被引：14

作者：

Qu, Haipeng ^{[1
]}

Yang, Sushan ^{[1
]}

Xu, Mingyao ^{[1
]}

An, Lijian ^{[1
]}

机构：

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

来源：

JOURNAL OF ALGEBRA | 2012年 / 358卷

关键词：

Minimal non-abelian p-groups; Metabelian p-groups; Regular p-groups; p-Groups of maximal class;

D O I：

10.1016/j.jalgebra.2012.03.007

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

For an odd prime p, we classify finite p-groups with a unique minimal non-abelian subgroup of index p. In fact, such groups have a maximal quotient which is a 3-group of maximal class. This paper is a part of classification of finite p-groups with a minimal non-abelian subgroup of index p, and partly solves a problem proposed by Berkovich. (C) 2012 Elsevier Inc. All rights reserved.

引用

页码：178 / 188

页数：11

共 50 条

[21] FINITE p-GROUPS ALL OF WHOSE MAXIMAL SUBGROUPS, EXCEPT ONE, HAVE ITS DERIVED SUBGROUP OF ORDER ≤p
Janko, Zvonimir
GLASNIK MATEMATICKI, 2012, 47 (02) : 325 - 332
[22] On the Hughes conjecture for some finite p-groups
Singh, Mandeep
Garg, Rohit
ANNALI DI MATEMATICA PURA ED APPLICATA, 2024, 203 (04) : 1783 - 1791
[23] ON AUTOMORPHISMS OF ORDER p OF METACYCLIC p-GROUPS WITHOUT CYCLIC SUBGROUPS OF INDEX p
Berkovich, Yakov
GLASNIK MATEMATICKI, 2009, 44 (02) : 343 - 348
[24] Finite p-groups whose nonnormal subgroups are metacyclic
Qiangwei Song
Haipeng Qu
ScienceChina(Mathematics), 2020, 63 (07) : 1271 - 1284
[25] FINITE p-GROUPS IN WHICH SOME SUBGROUPS ARE GENERATED BY ELEMENTS OF ORDER p
Berkovich, Yakov
GLASNIK MATEMATICKI, 2009, 44 (01) : 167 - 175
[26] The Central Extension of an Elementary Abelian p-Group by a Miniaml Non-Abelian p-Group
Lijian AN
Le YANG
Journal of Mathematical Research with Applications, 2016, 36 (04) : 457 - 466
[27] Finite nonabelian p-groups all of whose nonabelian maximal subgroups are either metacyclic or minimal nonabelian
Janko, Zvonimir
ARCHIV DER MATHEMATIK, 2011, 96 (02) : 105 - 107
[28] ON A1- AND A2-SUBGROUPS OF FINITE p-GROUPS
Berkovich, Yakov
Zhang, Qinhai
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2014, 13 (02)
[29] The number of conjugacy classes of nonnormal subgroups of finite p-groups
Li, Lili
Qu, Haipeng
JOURNAL OF ALGEBRA, 2016, 466 : 44 - 62
[30] Finite p-groups Which Have Many Normal Subgroups
Guo, Xiaoqiang
Liu, Qiumei
Zheng, Shiqiu
Feng, Lichao
INFORMATION COMPUTING AND APPLICATIONS, PT 1, 2010, 105 : 480 - 487

← 1 2 3 4 5 →