Prove that no proper nontrivial subgroup of Z is finite. (Z is the set of integers)
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Hint: are the subgroups of Z cyclic?
Originally Posted by dori1123 Prove that no proper nontrivial subgroup of Z is finite. (Z is the set of integers) Another way to think about it is that if is some finite subgroup of and then by Lagrange's theorem you know that . Now tell me, for what does that equation have a solution?
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.
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