# Left-quotient-transitively central factor

## Contents

BEWARE! This term is nonstandard and is being used locally within the wiki. [SHOW MORE]
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]

## Definition

A subgroup $H$ of a group $G$ is termed a left-quotient-transitively central factor if the following holds.

For any group $K$, normal subgroup $N$ with quotient map $\alpha:G \to G/N$, and isomorphism $\varphi:G \to K/N$, the following is true: if $N$ is a central factor of $G$, so is $\alpha^{-1}(\varphi(G))$.