Direct factor of fully characteristic subgroup

Symbol-free definition
A subgroup of a group is termed a direct factor of fully characteristic subgroup if it satisfies the following equivalent conditions:


 * It can be expressed as a direct factor of a fully characteristic subgroup.
 * It is a direct factor in its defining ingredient::fully characteristic closure.

In terms of the composition operator
The subgroup property of being a DFFC-subgroup is obtained by applying the composition operator to the subgroup properties of being a direct factor and of being fully characteristic.

Stronger properties

 * Weaker than::Fully characteristic subgroup
 * Weaker than::Direct factor

Weaker properties

 * Stronger than::Direct factor of characteristic subgroup
 * Stronger than::Central factor of characteristic subgroup
 * Stronger than::Normal subgroup of characteristic subgroup
 * Stronger than::2-subnormal subgroup
 * Stronger than::Subnormal subgroup