Left-quotient-transitively central factor

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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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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 $\phi :G\to K/N$, the following is true: if $N$ is a central factor of $G$, so is ${\alpha }^{-1}(\phi (G))$.

Relation with other properties

Weaker properties

• Central factor