Abelian groups with a minimal generating set

  • Pavel Ruzicka


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.

Quaestiones Mathematicae 33(2010), 147–159

Author Biography

Pavel Ruzicka
Charles University, Faculty of Mathematics and Physics, Department of Algebra, Sokolovská 83, 186 75 Praha 8, Czech Republic

Journal Identifiers

eISSN: 1727-933X
print ISSN: 1607-3606