Self-centralizing direct factor

Definition
A subgroup of a group is termed a self-centralizing direct factor if it satisfies the following equivalent conditions:


 * 1) It is both a self-centralizing subgroup (i.e., it contains its own centralizer) and a direct factor of the whole group.
 * 2) It is a direct factor of the whole group such that the quotient group is a centerless group.
 * 3) It is a direct factor of the whole group with a complement that is a centerless group.

Weaker properties

 * Stronger than::Centerless-quotient normal subgroup
 * Stronger than::Self-centralizing normal subgroup
 * Stronger than::Self-centralizing subgroup