# Right-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

### Definition with symbols

A subgroup of a group is termed a **right-quotient-transitively central factor** if is a normal subgroup of and whenever is a subgroup of such that is a central factor of , then is a central factor of .

## Relation with other properties

### Stronger properties

### Weaker properties

- Join-transitively central factor:
*For proof of the implication, refer Right-quotient-transitively central factor implies join-transitively central factor and for proof of its strictness (i.e. the reverse implication being false) refer Join-transitively central factor not implies right-quotient-transitively central factor*. - Central factor
- Transitively normal subgroup
- Normal subgroup