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Abelian Groups, Z-Modules and Q-Modules

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(6) If M is a finite abelian group then M is naturally a Z-module. Can this action be extended to make M into a Q-module?

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Solution Summary

Abelian Groups, Z-Modules and Q-Modules are investigated.

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Proof:
First, I show that M is naturally a Z-module. For any x in M and n in Z,
we can define nx=x^n=x*x*...*x (n times), where * is the operation in
group M. This definition makes sense ...

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