# Join-transitively central factor

From Groupprops

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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]

This is a variation of central factor|Find other variations of central factor |

## Definition

A subgroup of a group is termed a **join-transitively central factor** if its join with any central factor is a central factor. Note that since central factors are normal subgroups, and a join of a normal subgroup with another subgroup is the same as the product, this is equivalent to requiring that the product with any central factor is a central factor.

## Formalisms

### In terms of the join-transiter

This property is obtained by applying the join-transiter to the property: central factor

View other properties obtained by applying the join-transiter

## Relation with other properties

### Stronger properties

- Central subgroup:
`For full proof, refer: Central subgroup implies join-transitively central factor` - Direct factor:
`For full proof, refer: Direct factor implies join-transitively central factor` - Right-quotient-transitively central factor

### Weaker properties

- Central factor
- SCAB-subgroup
- Conjugacy-closed normal subgroup
- Transitively normal subgroup
- Normal subgroup