Finite p-Groups Whose Number of Subgroups of Each Order Is at most p4

被引：1

作者：

Wang, Lifang ^{[1
]}

机构：

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

来源：

ALGEBRA COLLOQUIUM | 2019年 / 26卷 / 03期

关键词：

finite p-groups; enumeration of subgroups; type of regular p-groups;

D O I：

10.1142/S1005386719000300

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Assume G is a group of order p(n), where p is an odd prime. Let s(k) (G) denote the number of subgroups of order p(k) of G. We give a criterion for a p-group to be with s(k) (G) <= p(4) for each integer k satisfying 1 <= k <= n. Moreover, such p-groups are classified.

引用

页码：411 / 424

页数：14

共 50 条

[21] Finite p-groups All of Whose Minimal Nonabelian Subgroups are Nonmetacyclic of Order p3
Qin Hai Zhang
Acta Mathematica Sinica, English Series, 2019, 35 : 1179 - 1189
[22] On subgroups of finite p-groups
Berkovich, Yakov
Janko, Zvonimir
ISRAEL JOURNAL OF MATHEMATICS, 2009, 171 (01) : 29 - 49
[23] On subgroups of finite p-groups
Yakov Berkovich
Zvonimir Janko
Israel Journal of Mathematics, 2009, 171 : 29 - 49
[24] On subgroups of finite p-groups
Berkovich, Y
JOURNAL OF ALGEBRA, 2000, 224 (02) : 198 - 240
[25] Finite p-groups all of whose maximal subgroups either are metacyclic or have a derived subgroup of order ≤ p
Lihua Zhang
Yanming Xia
Qinhai Zhang
Chinese Annals of Mathematics, Series B, 2015, 36 : 11 - 30
[26] Finite p-Groups all of Whose Maximal Subgroups Either are Metacyclic or Have a Derived Subgroup of Order ≤ p
Zhang, Lihua
Xia, Yanming
Zhang, Qinhai
CHINESE ANNALS OF MATHEMATICS SERIES B, 2015, 36 (01) : 11 - 30
[27] Finite p-Groups all of Whose Maximal Subgroups Either are Metacyclic or Have a Derived Subgroup of Order ≤ p
Lihua ZHANG
Yanming XIA
Qinhai ZHANG
Chinese Annals of Mathematics(Series B), 2015, 36 (01) : 11 - 30
[28] Finite p-groups of exponent pe all of whose cyclic subgroups of order pe are normal
Janko, Zvonimir
JOURNAL OF ALGEBRA, 2014, 416 : 274 - 286
[29] Finite p-groups all of whose maximal abelian subgroups are soft
Qu HaiPeng
SCIENCE CHINA-MATHEMATICS, 2010, 53 (11) : 3037 - 3040
[30] Finite p-Groups Whose Abelian Subgroups Have a Trivial Intersection
Shi Rong LI Department of Mathematics
ActaMathematicaSinica(EnglishSeries), 2007, 23 (04) : 731 - 734

← 1 2 3 4 5 →