MINIMAL NONABELIAN AND MAXIMAL SUBGROUPS OF A FINITE p-GROUP

被引：2

作者：

Berkovich, Yakov ^{[1
]}

机构：

[1] Univ Haifa, Dept Math, IL-31905 Haifa, Israel

来源：

GLASNIK MATEMATICKI | 2008年 / 43卷 / 01期

关键词：

Metacyclic p-groups; p-groups of maximal class; minimal non-abelian p-groups; absolutely regular p-groups; abelian maximal subgroups; maximal abelian normal subgroups;

D O I：

10.3336/gm.43.1.07

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The p-groups all of whose nonabelian maximal subgroups are either absolutely regular or of maximal class, are classified (Theorem 2.1). For the main result of [CP] and [ZAX] classifying the p-groups all of whose proper nonabelian subgroups are metacyclic, we offer a proof which is shorter and not so involved. In conclusion we study, in some detail, the p-groups containing an abelian maximal subgroup.

引用

页码：97 / 109

页数：13

共 49 条

[1] On the number of minimal nonabelian subgroups in a nonabelian finite p-group
Berkovich, Yakov
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2017, 16 (03)
[2] 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
[3] Finite p-groups with many minimal nonabelian subgroups
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JOURNAL OF ALGEBRA, 2012, 357 : 263 - 270
[4] ON THE NUMBER OF SUBGROUPS OF GIVEN TYPE IN A FINITE p-GROUP
Berkovich, Yakov
GLASNIK MATEMATICKI, 2008, 43 (01) : 59 - 95
[5] Finite p-groups All of Whose Minimal Nonabelian Subgroups are Nonmetacyclic of Order p
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Acta Mathematica Sinica,English Series, 2019, (07) : 1179 - 1189
[6] On the Wielandt Subgroup in a p-Group of Maximal Class
Xiaohong ZHANG1 Xiuyun GUO1 1Department of Mathematics
Chinese Annals of Mathematics(Series B), 2012, 33 (01) : 83 - 90
[7] Finite p-groups All of Whose Minimal Nonabelian Subgroups are Nonmetacyclic of Order p3
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ACTA MATHEMATICA SINICA-ENGLISH SERIES, 2019, 35 (07) : 1179 - 1189
[8] On the Wielandt Subgroup in a p-Group of Maximal Class
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Guo, Xiuyun
CHINESE ANNALS OF MATHEMATICS SERIES B, 2012, 33 (01) : 83 - 90
[9] THE NUMBER OF SUBGROUPS OF GIVEN ORDER IN A METACYCLIC p-GROUP
Berkovich, Yakov
GLASNIK MATEMATICKI, 2011, 46 (01) : 79 - 101
[10] Finite p-Groups with Few Nonabelian Subgroups of Possible Orders
Mi, Xiaoli
Zhang, Junqiang
BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2025, 51 (02)

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