Group theory and generalizations Infinite groups and combinatorial group theory Concept
Hopfian group
Summary
A group is Hopfian if every surjective homomorphism from the group to itself is an isomorphism. Equivalently, the group is not isomorphic to any of its proper quotients. Finite groups, and every finitely generated residually finite group are Hopfian. The Baumslag–Solitar group is a finitely presented group that is not Hopfian.
Further reading
About this page
| Tag | PHEN4E1JPT |
|---|---|
| URI | m2://PHEN4E1JPT |
| Kind | concept |
| Writing | W0 stub |
| MSC | 20E26, 20E36 |
| Specializes | Group |
| Same as | |
| Changed | 2 November 2026 |
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