K-group

Symbol-free definition
A group is termed a K-group if every subgroup of the group is lattice-complemented.

Definition with symbols
A group $$G$$ is termed a K-group if given any subgroup $$H$$ of $$G$$, there is a subgroup $$L$$ such that $$H \cap L$$ is trivial and the subgroup generated by $$H$$ and $$L$$ (viz $$$$) is $$G$$.

Stronger properties

 * Finite simple group
 * C-group
 * SK-group
 * SC-group

Weaker properties

 * Frattini-free group:

Metaproperties
A direct product of K-groups is a K-groups. Thus, the property of being a K-group is direct product-closed.

Facts
If a core-free maximal subgroup of a group is a K-group, then the whole group is a K-group.