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 ${\displaystyle HT=G}$ 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

References

• Y. Wang, c-normality of groups and its properties, Journal of Algebra, Vol. 180 (1996), 954-965