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.
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页码：397 / 405
页数：9
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