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

 Messages: [ Previous | Next ]
 Butch Malahide Posts: 894 Registered: 6/29/05
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 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}.

Date Subject Author
4/4/13 Kaba
4/4/13 Kaba
4/4/13 Kaba
4/4/13 Butch Malahide
4/5/13 Kaba
4/5/13 Brian Q. Hutchings
4/5/13 Kaba
4/5/13 Butch Malahide
4/5/13 Kaba
4/4/13 Butch Malahide
4/5/13 Kaba