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 50 条

[41] AUTOMORPHISM GROUP OF A P-GROUP OF MAXIMAL CLASS WITH AN ABELIAN MAXIMAL SUBGROUP
BAARTMANS, A
WOEPPEL, JJ
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (01): : A104 - A105
[42] The coexponent of a finite p-group
Bai, H
Ma, YJ
Zhang, JP
COMMUNICATIONS IN ALGEBRA, 2003, 31 (07) : 3497 - 3504
[43] BREADTH OF A FINITE P-GROUP
GALLIAN, JA
MATHEMATISCHE ZEITSCHRIFT, 1972, 126 (03) : 224 - &
[44] NUMBER OF ELEMENTARY ABELIAN SUBGROUPS OF A P-GROUP
JONAH, DW
KONVISSE.MW
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 20 (01): : A94 - A94
[45] FINITE p-GROUPS IN WHICH NORMAL CLOSURES FOR EVERY NONNORMAL SUBGROUPS ARE MINIMAL NONABELIAN
Yu, Dapeng
Chen, Guiyun
Xue, Haibo
Lv, Heng
ITALIAN JOURNAL OF PURE AND APPLIED MATHEMATICS, 2015, (34): : 431 - 436
[46] The intersection of nonabelian subgroups of finite p-groups
Zhang, Lihua
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2017, 16 (01)
[47] 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
[48] Normal p-subgroups of the automorphism group of an Abelian p-group
Abraham, RP
JOURNAL OF ALGEBRA, 1998, 199 (01) : 116 - 123
[49] On c-normal maximal and minimal subgroups of Sylow p-subgroups of finite groups
Xiuyun Guo
K. P. Shum
Archiv der Mathematik, 2003, 80 : 561 - 569
[50] On s-semipermutable maximal and minimal subgroups of Sylow p-subgroups of finite groups
Wang, LF
Wang, YM
COMMUNICATIONS IN ALGEBRA, 2006, 34 (01) : 143 - 149

← 1 2 3 4 5 →