# The torsion subset of a non-abelian group is not, in general, a subgroup.

The torsion subset T of G is the subset of G consisting of all elements that have finite order.

Let G be a finitely generated group with nontrivial finite derived subgroup.is the torsion subset T form a subgroup of G?

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What is a derived subgroup? –  Rasmus Nov 8 '12 at 14:23
What have you tried? Do you know the answer if the derived subgroup is trivial? –  jspecter Nov 8 '12 at 14:23
The derived subgroup of a group is the subgroup generated by all the commutators of the group. –  mojtaba farazi Nov 8 '12 at 14:27
If the derived subgroup be trivial then G is abelian group and clearly T is a form subgroup of G. –  mojtaba farazi Nov 8 '12 at 14:29
Well it's true in $G/G'$, and $G'$ is finite. –  Derek Holt Nov 8 '12 at 16:11