Complete characteristic subgroup

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This article describes a property that arises as the conjunction of a subgroup property: characteristic subgroup with a group property (itself viewed as a subgroup property): complete group
View a complete list of such conjunctions

Definition

A subgroup of a group is termed a complete characteristic subgroup or complete characteristic direct factor if it satisfies the following equivalent conditions:

  1. It is complete as a group and is a characteristic subgroup of the whole group.
  2. It is complete as a group and is a characteristic direct factor of the whole group.

Relation with other properties

Weaker properties