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?
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?
It works even more generally: if G' is included in T, then T is a subgroup of G.
And so, if T is not a subgroup of G then G has at least one commutator of infinite order.