Locally nilpotent groups with all subgroups normal-by-(finite rank)

被引：0

作者：

Longobardi, P ^{[1
]}

Maj, M ^{[1
]}

Smith, H ^{[1
]}

机构：

[1] Univ Naples, Dipartimento Matemat & Applicaz, I-80126 Naples, Italy

来源：

JOURNAL OF GROUP THEORY | 1998年 / 1卷 / 03期

关键词：

D O I：

暂无

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a locally nilpotent group in which H/Core(G)H has finite rank for all subgroups H. If G is torsion-free then G/Z(G) has finite rank. In general G has an abelian normal subgroup A with G/A of finite rank, and H/Core(G)H has bounded rank for all H. Further results are obtained in the case where H/Core(G)H has rank at most t (a fixed positive integer) for all subgroups H.

引用

页码：291 / 299

页数：9

共 50 条

[31] Nilpotent subgroups of groups with all subgroups subnormal
Casolo, C
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2003, 35 : 15 - 22
[32] Groups with all subgroups normal-by-finite
Buckley, JT
Lennox, JC
Neumann, BH
Smith, H
Wiegold, J
JOURNAL OF THE AUSTRALIAN MATHEMATICAL SOCIETY SERIES A-PURE MATHEMATICS AND STATISTICS, 1995, 59 : 384 - 398
[33] Finite simple groups the nilpotent residuals of all of whose subgroups are TI-subgroups
Meng, Wei
Lu, Jiakuan
Zhang, Boru
RICERCHE DI MATEMATICA, 2024, 73 (05) : 2605 - 2615
[34] Locally finite groups with a nilpotent or locally nilpotent maximal subgroup
Bruno, B
Napolitani, F
JOURNAL OF GROUP THEORY, 1999, 2 (04) : 393 - 399
[35] Finite groups with a system of nilpotent subgroups
Li, SR
Dark, RS
ALGEBRA COLLOQUIUM, 2005, 12 (02) : 199 - 204
[36] COUNTABLE LOCALLY NILPOTENT GROUPS OF FINITE EXPONENT WITHOUT MAXIMAL-SUBGROUPS
VAUGHANLEE, MR
WIEGOLD, J
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 1981, 13 (JAN) : 45 - 46
[37] Infinite locally finite groups with the locally nilpotent non-Dedekind norm of decomposable subgroups
Lukashova, Tetyana D.
COMMUNICATIONS IN ALGEBRA, 2020, 48 (03) : 1052 - 1057
[38] Locally graded groups with all non-nilpotent subgroups permutable, II
Atlihan, Sevgi
Dixon, Martyn R.
Evans, Martin J.
JOURNAL OF ALGEBRA, 2024, 641 : 530 - 533
[39] Generation of finite groups by nilpotent subgroups
Damian, E
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2003, 6B (01): : 245 - 255
[40] Conjugacy classes of non-normal subgroups in finite nilpotent groups
Fernandez-Alcober, Gustavo A.
Legarreta, Leire
JOURNAL OF GROUP THEORY, 2008, 11 (03) : 381 - 397

← 1 2 3 4 5 →