The question has been described in the title. How to prove it?
An infinite group is cyclic if and only if it is isomorphic to each of its non-trivial subgroups
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$\begingroup$
abstract-algebra
group-theory
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2It must be "to each of its proper *non-trivial* subgroups" – 2012-11-15
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0Hint: What are the simplest non-trivial subgroups? – 2012-11-15
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0Ah, I get it. Suddenly it turns out to be quite easy. – 2012-11-15
1 Answers
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Look at a cyclic subgroup generated by any element that is not the identity.