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]

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)).

Relation with other properties

Weaker properties