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Please forgive my ignorance here: let G be an infinite group, and let H be

a subgroup of G of finite index . Does H necessarily have torsion? I can

see if , e.g., G was Abelian with G=Z^n (+) Z/m , then , say, would have

subgroups of finite index, but I can't tell if this is an iff condition.

Any Ideas?

Thanks.

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# Finite-Index Subgroups of Infinite Groups.

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