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
