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 on c normal subgroups:

• Every normal subgroup is c normal
• Every retract is c normal
• Every c normal subgroup is weakly c normal