Upper join of direct factors

Definition
A subgroup $$H$$ of a group $$G$$ is termed an upper join of direct factors if there exist intermediate subgroups $$K_i, i \in I$$ of $$G$$ containing $$H$$, such that:


 * The join of the $$K_i$$s is equal to $$G$$.
 * $$H$$ is a direct factor in each of the $$K_i$$s.

Stronger properties

 * Weaker than::Direct factor

Weaker properties

 * Stronger than::Central factor
 * Stronger than::Transitively normal subgroup
 * Stronger than::Normal subgroup