Properties of groups | Infinite group theory

Hopfian group

In mathematics, a Hopfian group is a group G for which every epimorphism G → G is an isomorphism. Equivalently, a group is Hopfian if and 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 not isomorphic to any of its proper subgroups. (Wikipedia).

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Isomorphism | Finitely generated group | Finite group | Baumslag–Solitar group | Subgroup | Quotient group | Group homomorphism | Undecidable problem | Mathematics | Rational number | Real number | Residually finite group | Adian–Rabin theorem | Presentation of a group | Free group | Co-Hopfian group | Group (mathematics)