Consider the group (Q, +)/(Z, +), the group of rationals (under addition) modulo the subgroup of integers. So an element of this group is a coset a + Z where a is a rational number.
(a) Determine the order of the elemnt 3/4 + Z.
(b) Show that every element of this group has nite order.
(c) Prove that the group is innite.
(d) Prove that every nite subgroup is cyclic.