Quotient-divisibility-faithful subgroup

This article defines a subgroup property: a property that can be evaluated to true/false given a group and a subgroup thereof, invariant under subgroup equivalence. View a complete list of subgroup properties[SHOW MORE]

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Statement

A subgroup $H$ of a group $G$ is termed a quotient-divisibility-faithful subgroup if $H$ is a normal subgroup of $G$ and for any prime number $p$ such that the quotient group $G/H$ is $p$-divisible, $G$ is also $p$-divisible.

Facts

• Derived subgroup is quotient-divisibility-faithful in nilpotent group