
Re: Epimorphic groups
Posted:
Apr 4, 2013 8:46 PM


On Apr 4, 5:39 pm, Kaba <k...@nowhere.com> wrote: > > Let G, G', and H be groups with G a subgroup 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}.

