a) The inclusion Z -> R is a homomorphisms of additive groups.

b) The subgroup {0} of Z is isomorphic to the subgroup {(1)} of S5.

These are both true statements, but I must know how to prove them. Can someone show me please? Thanks.

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- October 22nd 2011, 05:58 PMjzelltHomomorphisms/Isomorphisms
a) The inclusion Z -> R is a homomorphisms of additive groups.

b) The subgroup {0} of Z is isomorphic to the subgroup {(1)} of S5.

These are both true statements, but I must know how to prove them. Can someone show me please? Thanks. - October 22nd 2011, 06:15 PMDrexel28Re: Homomorphisms/Isomorphisms
- October 22nd 2011, 06:20 PMjzelltRe: Homomorphisms/Isomorphisms
I'm not sure. If f is our function f: Z -> R, doesn't it have to be defined for me to continue?

- October 22nd 2011, 06:21 PMDrexel28Re: Homomorphisms/Isomorphisms
- October 22nd 2011, 06:25 PMjzelltRe: Homomorphisms/Isomorphisms
nevermind see next post...

- October 22nd 2011, 06:32 PMjzelltRe: Homomorphisms/Isomorphisms
So I googled it and it looks like the inclusion map of function f is defined by f(x) = x. So to show that f: Z->R is an homomorphism, I must show that f(x+y) = f(x) + f(y). But f(x+y) = x+y and f(x) + f(y) = x+y. So were done. COrrect?

- October 22nd 2011, 07:40 PMDrexel28Re: Homomorphisms/Isomorphisms