Suppose that , prove that

For this problem, I really don't have much clue, I feel I'm not too comfortable with the whole direct product thingy.

Thanks.

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- Sep 30th 2007, 02:12 PMtttcomraderExternal Direct Product isomorphism
Suppose that , prove that

For this problem, I really don't have much clue, I feel I'm not too comfortable with the whole direct product thingy.

Thanks. - Sep 30th 2007, 02:42 PMPlato
Did you understand this problem?

http://www.mathhelpforum.com/math-he...-products.html - Sep 30th 2007, 06:25 PMtttcomrader
No, I do not yet know how to solve that other problem as well. But I was hoping that by understanding how to solve this one, I might be able to solve the other one.

- Oct 1st 2007, 11:10 AMThePerfectHacker
There exists a bijective homomorphism and by definition.

Now create and similarly .

For , i.e. for some and . Define .

Show that is a mapping from into . Now show it is one-to-one and onto. Finally conclude by showing it is a homomorphism between these groups. It is a straightforward computation.