A note on groups of infinite rank whose proper subgroups are abelian-by-finite
Volume 137 / 2014
Colloquium Mathematicum 137 (2014), 165-170 MSC: Primary 20F22. DOI: 10.4064/cm137-2-2
It is proved that if $G$ is a locally (soluble-by-finite) group of infinite rank in which every proper subgroup of infinite rank contains an abelian subgroup of finite index, then all proper subgroups of $G$ are abelian-by-finite.