Complete direct factor

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This article describes a property that arises as the conjunction of a subgroup property: direct factor with a group property (itself viewed as a subgroup property): complete group
View a complete list of such conjunctions
This article describes a property that arises as the conjunction of a subgroup property: normal 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 direct factor or complete normal subgroup if it satisfies the following equivalent conditions:

  1. It is both a complete group (as a group by itself) and a normal subgroup of the whole group.
  2. It is both a complete group (as a group by itself) and a direct factor of the whole group.
  3. It is both a complete group (as a group by itself) and a complemented normal subgroup of the whole group.

Relation with other properties

Stronger properties

Weaker properties