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

[1] Groups in which each subnormal subgroup is commensurable with some normal subgroup
Dardano, Ulderico
De Mari, Fausto
JOURNAL OF GROUP THEORY, 2021, 24 (04) : 819 - 834
[2] Groups with many Subgroups which are Commensurable with some Normal Subgroup
Dardano, Ulderico
Rinauro, Silvana
ADVANCES IN GROUP THEORY AND APPLICATIONS, 2019, 7 : 3 - 13
[3] Groups in which all subgroups of infinite rank are subnormal
Kurdachenko, LA
Smith, H
GLASGOW MATHEMATICAL JOURNAL, 2004, 46 : 83 - 89
[4] GROUPS IN WHICH EVERY INFINITE SUBNORMAL SUBGROUP IS NORMAL
DEGIOVANNI, F
FRANCIOSI, S
JOURNAL OF ALGEBRA, 1985, 96 (02) : 566 - 580
[5] On groups in which every subgroup of infinite rank is subnormal of bounded defect
Evans, MJ
Kim, Y
COMMUNICATIONS IN ALGEBRA, 2004, 32 (07) : 2547 - 2557
[6] Groups in which each subgroup is commensurable with a normal subgroup
Casolo, Carlo
Dardano, Ulderico
Rinauro, Silvana
JOURNAL OF ALGEBRA, 2018, 496 : 48 - 60
[7] Groups of infinite rank with finite conjugacy classes of subnormal subgroups
De Falco, M.
de Giovanni, F.
Musella, C.
Trabelsi, N.
JOURNAL OF ALGEBRA, 2015, 431 : 24 - 37
[8] Groups in which every finite subnormal subgroup is normal
Chaboksavar, Masoud
de Giovanni, Francesco
RICERCHE DI MATEMATICA, 2015, 64 (02) : 331 - 338
[9] Groups in Which Every Normal Subgroup of Infinite Rank has Finite Index
De Falco, M.
de Giovanni, F.
Musella, C.
SOUTHEAST ASIAN BULLETIN OF MATHEMATICS, 2015, 39 (02) : 195 - 201
[10] Groups with almost normal subgroups of infinite rank
Semko N.N.
Kuchmenko S.N.
Ukrainian Mathematical Journal, 2005, 57 (4) : 621 - 639

← 1 2 3 4 5 →