Co-Hopfian group

In the mathematical subject of group theory, a co-Hopfian group is a group that is not isomorphic to any of its proper subgroups. The notion is dual to that of a Hopfian group, named after Heinz Hopf. 
Formal definition.
A group "G" is called co-Hopfian if whenever formula_1 is an injective group homomorphism then formula_2 is surjective, that is formula_3.