Divisibility-closed subgroup of abelian group

This article describes a property that arises as the conjunction of a subgroup property: divisibility-closed subgroup with a group property imposed on the ambient group: abelian group
View a complete list of such conjunctions | View a complete list of conjunctions where the group property is imposed on the subgroup

Definition

A subgroup $H$ of a group $G$ is termed a divisibility-closed subgroup of abelian group if $G$ is an abelian group and $H$ is a divisibility-closed subgroup of $G$, i.e., for any prime number $p$ such that $G$ is a $p$-divisible group, then $H$ is also a $p$-divisible group.