suppose that H is a subset of Group Z ,Give me a subset like H that is a torsion subgroup of Z ???

Answer 1

I suppose by Z you mean the set of integers.
the torsion subgroup T of the group Z is the subgroup of Z consisting of all elements that have finite order. That is, the subgroup of element a such that a^n = 1 for some n.

Therefore T = {-1, +1}

Answer 2

The above answer is using multiplication as the group operation, Z is not a group under multiplication since the inverses are not in Z. So the only torsion subgroup is the trivial subgroup.