GROUPS OF INFINITE RANK IN WHICH NORMALITY IS A TRANSITIVE RELATION

被引：15

作者：

De Falco, M. ^{[1
]}

De Giovanni, F. ^{[1
]}

Musella, C. ^{[1
]}

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

机构：

[1] Univ Naples Federico II, Dipartimento Matemat & Applicaz, I-80126 Naples, Italy

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

来源：

GLASGOW MATHEMATICAL JOURNAL | 2014年 / 56卷 / 02期

关键词：

BY-FINITE GROUPS; SUBGROUPS;

D O I：

10.1017/S0017089513000323

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Agroup is called a T-group if all its subnormal subgroups are normal. It is proved here that if G is a periodic (generalized) soluble group in which all subnormal subgroups of infinite rank are normal, then either G is a T-group or it has finite rank. It follows that if G is an arbitrary group whose Fitting subgroup has infinite rank, then G has the property T if and only if all its subnormal subgroups of infinite rank are normal.

引用

页码：387 / 393

页数：7

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