Hopfian group

Definition
A group is termed Hopfian if it satisfies the following equivalent conditions:


 * It is not isomorphic to the quotient group by any nontrivial normal subgroup (in short, it is not isomorphic to any of its proper quotients).
 * Every surjective endomorphism of it is an automorphism.

Incomparable properties

 * Co-Hopfian group