Let G = Z+Z10 (+ is direct sum) and let H = { g an element of G | |g|=∞ or |g|=1 }. Prove or disprove that H is a subgroup of G. [Subgroups that contain no elements of finite order besides the identity are called torsion-free subgroups. For example, Z+{0} is a torsion-free subgroup of G.] I really am stuck on this problem, if someone could help me with it, it would be great