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...

only if it is not isomorphic to any of its proper quotients. A group G is co-Hopfian if every monomorphism G → G is an isomorphism. Equivalently, G is...

In the branch of mathematics called category theory, a hopfian object is an object A such that any epimorphism of A onto A is necessarily an automorphism...

field of pure mathematics. Co-Hopfian group Cohomotopy group EHP spectral sequence Hopfian group Hopfian object Quantum group Alexandroff P., Hopf H. Topologie...

In particular the group G is Hopfian and co-Hopfian. The outer automorphism group Out(G) of G is isomorphic to the additive group of dyadic rationals...

finitely generated one-relator group that is not Hopfian and therefore not residually finite, for example the Baumslag–Solitar group B ( 2 , 3 ) = ⟨ a , b ∣...

Gilbert; Solitar, Donald (1962), "Some two-generator one-relator non-Hopfian groups", Bulletin of the American Mathematical Society, 68 (3): 199–201, doi:10...

automorphism of M. This says simply that M is a Hopfian module. Similarly, an Artinian module M is coHopfian: any injective endomorphism f is also a surjective...