Uncountable groups in which normality is a transitive relation

被引：6

作者：

De Falco, M. ^{[1
]}

De Giovanni, F. ^{[1
]}

Musella, C. ^{[1
]}

Sysak, Y. P. ^{[2
]}

机构：

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

[2] Ukrainian Natl Acad Sci, Inst Math, Vul Tereshchenkivska 3, UA-01601 Kiev, Ukraine

来源：

INTERNATIONAL JOURNAL OF ALGEBRA AND COMPUTATION | 2019年 / 29卷 / 04期

关键词：

Uncountable group; subnormal subgroup; T-group; SUBGROUPS;

D O I：

10.1142/S0218196719500188

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A group is called a T-group if all its subnormal subgroups are normal. It is proved here that if G is an uncountable soluble periodic group of regular cardinality aleph in which all subnormal subgroups of cardinality aleph are normal, then G is a T-group, provided that it satisfies a suitable residual condition. An example shows that this latter restriction cannot be avoided.

引用

页码：627 / 638

页数：12

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