Finite p-groups in which the normalizer of each nonnormal subgroup is small

被引：0

作者：

Zhao, Libo ^{[1
]}

Li, Yangming ^{[1
]}

Gong, Lu ^{[2
]}

Guo, Xiuyun ^{[3
]}

机构：

[1] Guangdong Univ Educ, Coll Math, Guangzhou 510310, Peoples R China

[2] Nantong Univ, Sch Math & Stat, Nantong 226019, Jiangsu, Peoples R China

[3] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

来源：

HACETTEPE JOURNAL OF MATHEMATICS AND STATISTICS | 2024年 / 53卷 / 06期

基金：

美国国家科学基金会;

关键词：

non-Dedekindian p-group; the center; nonnormal subgroup;

D O I：

10.15672/hujms.1362734

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a finite non-Dedekindian p-group which satisfies NG(H) = HZ(G) for each nonnormal subgroup H , and we call it an NS-group. In this paper, it is proved that an NS-group is the product of a minimal nonabelian group and the center.

引用

页码：1642 / 1646

页数：5

共 50 条

[1] FINITE P-GROUPS IN WHICH EACH SUBGROUP OF COMMUTATORS SUBGROUP IS INVARIANT
SUBBOTIN, IY
DOPOVIDI AKADEMII NAUK UKRAINSKOI RSR SERIYA A-FIZIKO-MATEMATICHNI TA TECHNICHNI NAUKI, 1974, (12): : 1072 - 1074
[2] Finite p-groups in which the intersection of nonnormal subgroup and center has bounded order
Zhao, Libo
Li, Yangming
Gong, Lu
Guo, Xiuyun
COMMUNICATIONS IN ALGEBRA, 2023, 51 (09) : 3825 - 3833
[3] Finite non-solvable groups in which the normalizer of every nonnormal cyclic subgroup is maximal
Cao, Jianji
Guo, Xiuyun
Shum, K. P.
COMMUNICATIONS IN ALGEBRA, 2018, 46 (01) : 325 - 334
[4] FINITE p-GROUPS IN WHICH THE NORMALIZER OF EVERY NON-NORMAL SUBGROUP IS CONTAINED IN ITS NORMAL CLOSURE
Bai, Pengfei
Guo, Xiuyun
Wang, Junxin
BULLETIN OF THE KOREAN MATHEMATICAL SOCIETY, 2018, 55 (06) : 1835 - 1843
[5] Finite p-groups in which the cores of all the nonnormal subgroups are in the center
Zhao, Libo
Li, Yangming
Gong, Lue
Guo, Xiuyun
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, 2024,
[6] ON FINITE P-GROUPS IN WHICH SUBGROUP-PERMUTABILITY IS TRANSITIVE
BIANCHI, M
MAURI, AGB
VERARDI, L
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 1995, 9B (01): : 61 - 76
[7] FINITE p-GROUPS IN WHICH THE NORMAL CLOSURE OF EACH NON-NORMAL CYCLIC SUBGROUP IS NONABELIAN
Janko, Zvonimir
GLASNIK MATEMATICKI, 2014, 49 (02) : 333 - 336
[8] NOMALIZERS OF NONNORMAL SUBGROUPS OF FINITE p-GROUPS
Zhang, Qinhai
Gao, Juan
JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2012, 49 (01) : 201 - 221
[9] 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
[10] Finite p-groups whose nonnormal subgroups are metacyclic
Qiangwei Song
Haipeng Qu
Science China Mathematics, 2020, 63 : 1271 - 1284

← 1 2 3 4 5 →