Quotient-powering-invariant 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]

|Get subgroup property lookup help |Get exploration suggestions
VIEW RELATED: Subgroup property implications | Subgroup property non-implications | Subgroup metaproperty satisfactions | Subgroup metaproperty dissatisfactions | Subgroup property satisfactions |Subgroup property dissatisfactions
VIEW FACTS THAT:use, or start with, a subgroup satisfying the property|prove, or show that, a subgroup satisfies the property

Definition

A normal subgroup $H$ of a group $G$ is termed a quotient-powering-invariant subgroup if, for any prime number $p$ such that $G$ is a powered for $p$, the quotient group $G/H$ is also powered for $p$.

Relation with other properties

Stronger properties

Property	Meaning	Proof of implication	Proof of strictness (reverse implication failure)	Intermediate notions
normal subgroup of finite group
normal subgroup of periodic group
normal subgroup of finite index