Join-transitively central factor

Definition
A subgroup of a group is termed a join-transitively central factor if its join with any variation of::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.

Stronger properties

 * Weaker than::Central subgroup:
 * Weaker than::Direct factor:
 * Weaker than::Right-quotient-transitively central factor

Weaker properties

 * Stronger than::Central factor
 * Stronger than::SCAB-subgroup
 * Stronger than::Conjugacy-closed normal subgroup
 * Stronger than::Transitively normal subgroup
 * Stronger than::Normal subgroup