ON GROUPS IN WHICH SUBNORMAL SUBGROUPS OF INFINITE RANK ARE COMMENSURABLE WITH SOME NORMAL SUBGROUP

被引：1

作者：

Dardano, Ulderico ^{[1
]}

De Mari, Fausto ^{[1
]}

机构：

[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz R Caccioppoli, Via Cintia Monte S Angelo, I-80126 Naples, Italy

来源：

INTERNATIONAL JOURNAL OF GROUP THEORY | 2022年 / 11卷 / 01期

关键词：

transitivity; core-finite; normal-by-finite; close to normal;

D O I：

10.22108/ijgt.2021.127143.1671

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study soluble groups G in which each subnormal subgroup H with infinite rank is commensurable with a normal subgroup, i.e. there exists a normal subgroup N such that H boolean AND N has finite index in both H and N. We show that if such a G is periodic, then all subnormal subgroups are commensurable with a normal subgroup, provided either the Hirsch-Plotkin radical of G has infinite rank or G is nilpotent-by-abelian (and has infinite rank).

引用

页码：37 / 42

页数：6

共 50 条

[21] GROUPS OF INFINITE RANK WITH NORMALITY CONDITIONS ON SUBGROUPS WITH SMALL NORMAL CLOSURE
De Luca, Anna Valentina
Di Grazia, Giovanna
BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 2016, 94 (01) : 48 - 53
[22] Finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup
Shi, Jiangtao
Zhang, Cui
ARCHIV DER MATHEMATIK, 2013, 101 (02) : 101 - 104
[23] Finite groups in which every subgroup is a subnormal subgroup or a TI-subgroup
Jiangtao Shi
Cui Zhang
Archiv der Mathematik, 2013, 101 : 101 - 104
[24] On the structure of some non-periodic groups whose subgroups of infinite special rank are transitively normal
Velychko, T. V.
CARPATHIAN MATHEMATICAL PUBLICATIONS, 2021, 13 (02) : 515 - 521
[25] GROUPS WITH NORMAL SUBGROUPS POSSESSING SUBNORMAL COMPLEMENTS
TOH, KH
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1973, 41 (02) : 378 - 380
[26] On Groups whose Subnormal Abelian Subgroups are Normal
Kurdachenko, L. A.
Otal, J.
Subbotin, I. Ya
ADVANCES IN GROUP THEORY AND APPLICATIONS, 2022, 14 : 67 - 94
[27] Groups in which all Subgroups are Subnormal-by-Finite
Casolo, Carlo
ADVANCES IN GROUP THEORY AND APPLICATIONS, 2016, 1 : 33 - 45
[28] Groups in which every subgroup is f-subnormal
Casolo, C
Mainardis, M
JOURNAL OF GROUP THEORY, 2001, 4 (03) : 341 - 365
[29] Normal subgroups of groups which split over the infinite cyclic group
Moon, M
BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2000, 32 : 78 - 84
[30] ON THE INFLUENCE OF TRANSITIVELY NORMAL SUBGROUPS ON THE STRUCTURE OF SOME INFINITE GROUPS
Kurdachenko, Leonid A.
Otal, Javier
PUBLICACIONS MATEMATIQUES, 2013, 57 (01) : 83 - 106

← 1 2 3 4 5 →