Complemented characteristic subgroup

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This page describes a subgroup property obtained as a conjunction (AND) of two (or more) more fundamental subgroup properties: permutably complemented subgroup and characteristic subgroup
View other subgroup property conjunctions | view all subgroup properties

Definition

Symbol-free definition

A subgroup of a group is termed a complemented characteristic subgroup if it satisfies the following equivalent conditions:

  1. It is a characteristic subgroup as well as a permutably complemented subgroup.
  2. It is a characteristic subgroup as well as a lattice-complemented subgroup.
  3. It is a characteristic subgroup as well as a complemented normal subgroup, i.e., it occurs as the normal subgroup part in an internal semidirect product.

Relation with other properties

Stronger properties

Weaker properties