A note on commutator subgroups in groups of large cardinality

被引：2

作者：

De Falco, Maria ^{[1
]}

de Giovanni, Francesco ^{[1
]}

Musella, Carmela ^{[1
]}

机构：

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

来源：

MONATSHEFTE FUR MATHEMATIK | 2020年 / 191卷 / 02期

关键词：

Uncountable group; Commutator subgroup; Normality;

D O I：

10.1007/s00605-019-01302-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

If G is an uncountable group of regular cardinality aleph, we shall denote by LL aleph(G) the set of all subgroups of G of cardinality aleph. The aim of this paper is to describe the behaviour of groups G for which the set C aleph(G)={X '|X is an element of LL aleph(G)} is finite, at least when G is locally graded and has no simple sections of cardinality aleph. Among other results, it is proved that such a group has a finite commutator subgroup, provided that it contains an abelian subgroup of cardinality aleph.

引用

页码：249 / 256

页数：8

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