Originally Posted by
DanielThrice Consider the (additive) factor group Q/Z.
(a) Show that every coset of Z in Q contains exactly one representative q ∈ Q in the range0 ≤ q < 1.
(b) Show that every element of Q/Z has ﬁnite order, but there are elements of arbitrarily large order.
(c) Show that Q/Z is the torsion subgroup of R/Z.
(d) Show that Q/Z is isomorphic to the multiplicative group U∗ consisting of all roots of unityin C. (That is, U∗ = {z ∈ C|z^n = 1 for some n ∈ Z+}.)
I got a and b, but I can't figure out c or d, any help?