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

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 Kaba Posts: 289 Registered: 5/23/11
Re: Epimorphic groups
Posted: Apr 5, 2013 5:32 AM

5.4.2013 3:46, Butch Malahide wrote:
> 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}.

Thanks for this too.

--
http://kaba.hilvi.org

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