The only subgroup of finite order of a an infinite group is the identity

My proof

Let G be a group with infinite order

let H be a subgroup and let and

which make H with an infinite order

am I rite ?

is there any counter example

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- Dec 12th 2011, 09:26 PMAmerFinite subgroup of an infinite Group
The only subgroup of finite order of a an infinite group is the identity

My proof

Let G be a group with infinite order

let H be a subgroup and let and

which make H with an infinite order

am I rite ?

is there any counter example - Dec 13th 2011, 12:14 AMFernandoRevillaRe: Finite subgroup of an infinite Group
- Dec 13th 2011, 04:16 AMDrexel28Re: Finite subgroup of an infinite Group
More generally, take any field then if there exists non-zero with (i.e. a non-trivial root of unity) then the group of -roots of unity form a finite subgroup of . This clearly generalizes Dr.

**Revilla**'s example (so that, for example, the -roots of unity in ).

But, perhaps even more of a trivial counterexample. Take any infinite group and consider ....(Evilgrin) - Dec 13th 2011, 04:26 AMAmerRe: Finite subgroup of an infinite Group
Thanks