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

References

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

Mathematics Encyclopedia