ABELIAN GROUPS WITH A MINIMAL GENERATING SET

被引：4
|
作者：
Ruzicka, Pavel [1 ]
机构：
[1] Charles Univ Prague, Fac Math & Phys, Dept Algebra, Prague 18675 8, Czech Republic
来源：
QUAESTIONES MATHEMATICAE | 2010年 / 33卷 / 02期
关键词：
Minimal generating set; Abelian group; quotient; subgroup; product; uncountable; torsion; torsion-free;
D O I：
10.2989/16073606.2010.490991
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We study the existence of minimal generating sets in Abelian groups. We prove that Abelian groups with minimal generating sets are not closed under quotients, nor under subgroups, nor under infinite products. We give necessary and sufficient conditions for existence of a minimal generating set providing that the Abelian group is uncountable, torsion, or torsion-free completely decomposable.
引用
收藏
页码：147 / 159
页数：13
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