Perfect characteristic subgroup

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): perfect group
View a complete list of such conjunctions

Definition

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

1. It is perfect as a group and is a characteristic subgroup of the whole group.
2. It is a characteristic subgroup of the whole group contained in the perfect core of the whole group.

Relation with other properties

Weaker properties

• Perfect IA-automorphism-invariant subgroup
• IA-balanced subgroup
• Perfect normal subgroup
• Perfect subnormal subgroup