# Cocentral implies right-quotient-transitively central factor

From Groupprops

This article gives the statement and possibly, proof, of an implication relation between two subgroup properties. That is, it states that every subgroup satisfying the first subgroup property (i.e., cocentral subgroup) must also satisfy the second subgroup property (i.e., right-quotient-transitively central factor)

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## Contents

## Statement

Suppose is a group and is a cocentral subgroup of . Then, if is a subgroup of containing such that is a central factor of , is also a central factor of .

## Related facts

- Central implies join-transitively central factor
- Direct factor implies right-quotient-transitively central factor

## Facts used

## Proof

**PLACEHOLDER FOR INFORMATION TO BE FILLED IN**: [SHOW MORE] (essentially follows from facts (1) and (2)).