Finite groups with σ-Frobenius condition for non-normal σ-primary subgroups

被引：0

作者：

Hu, Bin ^{[1
]}

Huang, Jianhong ^{[1
]}

Skiba, Alexander N. ^{[2
]}

机构：

[1] Jiangsu Normal Univ, Sch Math & Stat, Xuzhou 221116, Jiangsu, Peoples R China

[2] Francisk Skorina Gomel State Univ, Dept Math & Technol Programming, Gomel 246019, BELARUS

来源：

JOURNAL OF ALGEBRA AND ITS APPLICATIONS | 2020年 / 19卷 / 03期

关键词：

Finite group; sigma-soluble group; sigma-nilpotent group; the sigma-Frobenius condition; m(sigma)-covering subgroup;

D O I：

10.1142/S0219498820500474

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let sigma = {sigma(i) vertical bar i is an element of I} be a partition of the set P of all primes and C a finite group. A group is said to be sigma-primary if it is a finite sigma(i)-group for some i. We say that a sigma(i)-subgroup H of G satisfies the sigma-Frobenius condition in G if N-G(H)/C-G(H) is a sigma(i)-group. In this paper, we determine the structure of finite groups in which every non-normal sigma-primary subgroup satisfies the sigma-Frobenius condition.

引用

页数：13

共 50 条

[41] FINITE p-GROUPS WHOSE NORMAL CLOSURES OF NON-NORMAL SUBGROUPS HAVE TWO ORDERS
Wang, Lifang
[J]. JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, 2022, 59 (04) : 805 - 819
[42] Finite non-nilpotent groups with two conjugacy classes of non-normal non-cyclic subgroups
Brandl, Rolf
Rezazadeh, Zahra
Taeri, Bijan
[J]. PUBLICATIONES MATHEMATICAE-DEBRECEN, 2020, 96 (3-4): : 459 - 474
[43] Groups with a bounded number of conjugacy classes of non-normal subgroups
La Haye, R
Rhemtulla, A
[J]. JOURNAL OF ALGEBRA, 1999, 214 (01) : 41 - 63
[44] Morita equivalent blocks in non-normal subgroups and p-radical blocks in finite groups
Hida, A
Koshitani, S
[J]. JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES, 1999, 59 : 541 - 556
[45] FC-groups with Few Subnormal Non-normal Subgroups
Mattia Brescia
[J]. Mediterranean Journal of Mathematics, 2022, 19
[46] NILPOTENT GROUPS WITH THREE CONJUGACY CLASSES OF NON-NORMAL SUBGROUPS
Mousavi, H.
[J]. BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY, 2014, 40 (05) : 1291 - 1300
[47] Finite p-groups whose non-normal cyclic subgroups have cyclic quotient groups in their normalizers
Wang, Jiao
[J]. RICERCHE DI MATEMATICA, 2023,
[48] The number of conjugacy classes of non-normal subgroups in nilpotent groups
Poland, J
Rhemtulla, A
[J]. COMMUNICATIONS IN ALGEBRA, 1996, 24 (10) : 3237 - 3245
[49] Groups with Finitely Many Isomorphism Classes of Non-Normal Subgroups
Kurdachenko, L. A.
Longobardi, P.
Maj, M.
[J]. ADVANCES IN GROUP THEORY AND APPLICATIONS, 2020, 10 : 9 - 41
[50] FC-groups with Few Subnormal Non-normal Subgroups
Brescia, Mattia
[J]. MEDITERRANEAN JOURNAL OF MATHEMATICS, 2022, 19 (05)

← 1 2 3 4 5 →