C-normal subgroup

In mathematics, in the field of group theory, a subgroup $$H$$ of a group $$G$$ is called c-normal if there is a normal subgroup $$T$$ of $$G$$ such that $$HT = G$$ and the intersection of $$H$$ and $$T$$ lies inside the normal core of $$H$$.

For a weakly c-normal subgroup, we only require $$T$$ to be subnormal.

Here are some facts about c-normal subgroups:


 * Every normal subgroup is c-normal
 * Every retract is c-normal
 * Every c-normal subgroup is weakly c-normal