Direct factor of characteristic subgroup

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


 * It can be expressed as a direct factor of a characteristic subgroup
 * It is a direct factor in its characteristic closure

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

Stronger properties

 * Weaker than::Characteristic subgroup
 * Weaker than::Direct factor
 * Weaker than::Minimal normal subgroup
 * Weaker than::Direct factor of fully characteristic subgroup
 * Weaker than::Direct root of characteristic subgroup

Weaker properties

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

Related properties

 * Characteristic subgroup of direct factor