Complete direct factor
From Groupprops
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
Contents
Definition
A subgroup of a group is termed a complete direct factor or complete normal subgroup if it satisfies the following equivalent conditions:
- It is both a complete group (as a group by itself) and a normal subgroup of the whole group.
- It is both a complete group (as a group by itself) and a direct factor of the whole group.
- It is both a complete group (as a group by itself) and a complemented normal subgroup of the whole group.
