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Topic: Epimorphic groups
Replies: 10   Last Post: Apr 5, 2013 3:37 PM

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Butch Malahide

Posts: 894
Registered: 6/29/05
Re: Epimorphic groups
Posted: Apr 4, 2013 8:46 PM
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On Apr 4, 5:39 pm, Kaba <> wrote:
> Let G, G', and H be groups with G a sub-group of G'. Let G and G' both
> be epimorphic (surjectively homomorphic) to H, with equal kernels for
> the epimorphisms. Does it then follow that G = G'?

No. Let G' = H = Z, let G be a nontrivial proper subgroup of G', and
let f:G --> H and f':G' --> H be isomorphisms; both kernels are equal
to {0}.

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