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.
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页码：249 / 256
页数：8
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