Groups satisfying the minimal condition on subgroups which are not transitively normal

被引：5

作者：

de Giovanni, F. ^{[1
]}

Kurdachenko, L. A. ^{[2
]}

Russo, A. ^{[3
]}

机构：

[1] Univ Napoli Federico II, Dipartimento Matemat & Applicaz, Via Cintia, Naples, Italy

[2] Natl Univ Dnipro, Dept Algebra, Dnipro, Ukraine

[3] Univ Campania Luigi Vanvitelli, Dipartimento Matemat & Fis, Via Vivaldi, Caserta, Italy

来源：

RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO | 2022年 / 71卷 / 01期

关键词：

T-group; (T)over-bar-group; Transitively normal subgroup;

D O I：

10.1007/s12215-021-00602-0

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A subgroup X of a group G is called transitively normal if X is normal in any subgroup Y of G such that X <= Y and X is subnormal in Y. Thus all subgroups of a group G are transitively normal if and only if normality is a transitive relation in every subgroup of G (i.e. G is a T-group). It is proved that a group G with no infinite simple sections satisfies the minimal condition on subgroups that are not transitively normal if and only if either G is Cernikov or a T-group.

引用

页码：397 / 405

页数：9

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