Finite injective endomorphism-invariant subgroup

Definition
A subgroup of a group is termed a finite injective endomorphism-invariant subgroup if it satisfies the following equivalent conditions:


 * 1) It is finite as a group and is an injective endomorphism-invariant subgroup of the whole group: every injective endomorphism of the whole group sends the subgroup to itself.
 * 2) It is finite as a group and is an conjunction involving::injective endomorphism-quotient-balanced subgroup of the whole group: every injective endomorphism of the whole group induces an injective endomorphism on the quotient group.

Stronger properties

 * Weaker than::Finite fully invariant subgroup
 * Weaker than::Characteristic subgroup of finite group

Weaker properties

 * Stronger than::Finite characteristic subgroup