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.
Did you understand this problem?
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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.