Hopfian group

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In mathematics, a Hopfian group is a group G for which every epimorphism

GG

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

GG

is an isomorphism. Equivalently, G is not isomorphic to any of its proper subgroups.

Examples of Hopfian groups[edit]

Examples of non-Hopfian groups[edit]

References[edit]

External links[edit]