Hi,

i'm trying to construct an construct an epimorphism from and from but unfortunately i have no idea how to start...

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- Dec 12th 2013, 02:53 PMsurryconstruct an epimorphism
Hi,

i'm trying to construct an construct an epimorphism from and from but unfortunately i have no idea how to start... - Dec 12th 2013, 04:30 PMHallsofIvyRe: construct an epimorphism
For a in and n in Z, map (a, n) to n. That's trivial.

For what do you mean by " " and " "? My first thought was that " " was the set of permutations on 3 objects and " " was the set of pairs of complex numbers but in that case, is**finite**(containing 6 members) while is infinite so there**cannot**be such an epimorphism. - Dec 12th 2013, 04:32 PMSlipEternalRe: construct an epimorphism
You haven't given enough information. The morphism is an epimorphism for the first one. The morphism is an epimorphism for the second one. I am not sure what more you are trying to do with this. If you want, you can use which would also be an epimorphism for the first one.

- Dec 12th 2013, 04:34 PMSlipEternalRe: construct an epimorphism
- Dec 12th 2013, 04:40 PMromsekRe: construct an epimorphism

maybe this?

from here

That's Integers Z, I didn't notice a Tex code for it. - Dec 16th 2013, 01:17 PMDevenoRe: construct an epimorphism
An explicit epimorphism , where :

Proving this is a homomorphism is the tricky part, it may be easier to observe that what we are actually doing is mapping:

, which is isomorphic to any cyclic group of order 2, since it is of order 2 (any two groups of prime order are isomorphic and both are cyclic).