Prove the internal direct product criterion which was mentioned in classed (without proof): Let G be a group and G,..., Gn be normal subgroups of G. G=G ... Gn if and only if the following two conditions hold: G=G...Gn, where recall G...G is the collection of all elements of G of the form gi.... 9n where for each 1 i n, gi E Gi. For all 1 i n, Gin (G...Gi-1G+1...Gn) = {id}.