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Post Closed as "too localized" by Ryan Budney, J.C. Ottem, Ian Agol, Felipe Voloch, Pete L. Clark
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Todd Trimble
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Is there an infinite (edit: but finitely generated) group G such that for all g in G, |g| is finite?

If so, how many such groups exist?

Is there an infinite group G such that for all g in G, |g| is finite?

If so, how many such groups exist?

Is there an infinite (edit: but finitely generated) group G such that for all g in G, |g| is finite?

If so, how many such groups exist?

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wjomlex
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Is there an infinite group whose elements all have finite order?

Is there an infinite group G such that for all g in G, |g| is finite?

If so, how many such groups exist?