C-normal subgroup explained

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

References

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