Examples of groups The non-zero rationals under multiplication G=Q-0}={ab} a b non-zero integers the group operator is ">> ordinary multiplication If a/b, c/d are in Q-0f thena/b*c/d=(ac/bd)is in Q-10) the identity is 1 the inverse of a/b is b/a the rationals are associative the rationals are commutative(so the group is abelianExamples of Groups The non-zero rationals under multiplication G = Q -{0} = {a/b} a,b non-zero integers the group operator is “*”, ordinary multiplication • If a/b, c/d are in Q-{0}, then a/b * c/d = (ac/bd) is in Q-{0} • the identity is 1 • the inverse of a/b is b/a • the rationals are associative • the rationals are commutative (so the group is abelian)