π-Quasinormally embedded subgroups and p-nilpotency of finite groups

被引：1

作者：

Xu, Yong ^{[1
]}

Chen, Guiyun ^{[2
]}

机构：

[1] Henan Univ Sci & Technol, Sch Math & Stat, Luoyang, Henan, Peoples R China

[2] Southwest Univ, Sch Math & Stat, Chongqing 400715, Peoples R China

来源：

COMMUNICATIONS IN ALGEBRA | 2021年 / 49卷 / 01期

基金：

中国国家自然科学基金; 中国博士后科学基金;

关键词：

Finite group; p-nilpotency; pi-quasinormally embedded subgroup; MAXIMAL-SUBGROUPS; SYLOW SUBGROUPS; NORMALITY;

D O I：

10.1080/00927872.2020.1800721

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let P be a nontrivial p-group. A chain of subgroups 1 = P-0 <= P-1 <= . . . <= P-n - P is called a maximal chain of P provided that vertical bar P-i : Pi-1 vertical bar = p, i = 1, 2, ... , n: In this article, we determine the structure of finite groups having pi-quasinormally embedded subgroups of a maximal chain of Sylow subgroups. We obtain new characterizations of finite p-nilpotent and supersolvable groups.

引用

页码：421 / 426

页数：6

共 16 条

[1] Some results on p-nilpotence and supersolvability of finite groups [J].

Asaad, M. .

COMMUNICATIONS IN ALGEBRA, 2006, 34 (11) :4217-4224

[2] INFLUENCE OF PI-QUASINORMALITY ON MAXIMAL-SUBGROUPS OF SYLOW SUBGROUPS OF FITTING SUBGROUP OF A FINITE-GROUP [J].

ASAAD, M ;

RAMADAN, M ;

SHAALAN, A .

ARCHIV DER MATHEMATIK, 1991, 56 (06) :521-527

[3] On S-quasinormally embedded subgroups of finite groups [J].

Asaad, M ;

Heliel, AA .

JOURNAL OF PURE AND APPLIED ALGEBRA, 2001, 165 (02) :129-135

[4] On minimal subgroups of finite groups [J].

Ballester-Bolinches, A ;

Pedraza-Aguilera, MC .

ACTA MATHEMATICA HUNGARICA, 1996, 73 (04) :335-342

[5] Sufficient conditions for supersolubility of finite groups [J].

Ballester-Bolinches, A ;

Pedraza-Aguilera, MC .

JOURNAL OF PURE AND APPLIED ALGEBRA, 1998, 127 (02) :113-118

[6] FINITE GROUPS WHOSE MINIMAL SUBGROUPS ARE NORMAL [J].

BUCKLEY, J .

MATHEMATISCHE ZEITSCHRIFT, 1970, 116 (01) :15-&

[7]

Deskins W. E., 1963, MATH Z, V82, P125, DOI [DOI 10.1007/BF01111801, 10.1007/BF01111801]

[8]

Doerk K., 1992, FINITE SOLVABLE GROU

[9]

Huppert, 1967, ENDLICHE GRUPP

[10]

KEGEL O. H., 1962, Math. Z., V78, P205, DOI DOI 10.1007/BF01195169

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