Prove that no proper nontrivial subgroup of Z is finite. (Z is the set of integers)

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- Jul 17th 2011, 04:09 PMdori1123Prove that no proper nontrivial subgroup of Z is finite.
Prove that no proper nontrivial subgroup of Z is finite. (Z is the set of integers)

- Jul 17th 2011, 05:12 PMModusPonensRe: Prove that no proper nontrivial subgroup of Z is finite.
Hint: are the subgroups of Z cyclic?

- Jul 17th 2011, 10:57 PMDrexel28Re: Prove that no proper nontrivial subgroup of Z is finite.
- Jul 18th 2011, 12:11 AMFernandoRevillaRe: Prove that no proper nontrivial subgroup of Z is finite.
Another way: if is a subgroup of , use the Euclidean Division to prove that for some .

P.S. Of course, this way provides unnecessary information with respect to the initial question.