Right-transitively lattice-complemented subgroup

Symbol-free definition
A subgroup of a group is termed a right-transitively lattice-complemented subgroup if every lattice-complemented subgroup of the subgroup is also a lattice-complemented subgroup of the whole group.

Definition with symbols
A subgroup $$H$$ of a group $$G$$ is termed a right-transitively lattice-complemented subgroup if, for any lattice-complemented subgroup $$K$$ of $$H$$, $$K$$ is also lattice-complemented in $$G$$.

Stronger properties

 * Weaker than::Retract
 * Weaker than::Direct factor
 * Weaker than::Free factor

Weaker properties

 * Stronger than::Lattice-complemented subgroup

Related properties

 * Right-transitively permutably complemented subgroup