(1) (25 points) Let G denote a group with identity element denoted by e, and let a, b E G denote two commmuting elements of G (i.e. ab 2 ba). (a) Dene a subset of G by = {aibj : i,j E Z}. Show that is a subgroup of G. (b) Suppose that 0(G) 2 pg where p, q are prime numbers. Show that if a 3A 6, and bis not contained in 7 then = G