Self-centralizing direct factor

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: self-centralizing subgroup and direct factor
View other subgroup property conjunctions | view all subgroup properties


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.

Relation with other properties

Weaker properties