Look in a math book? Show that cosets partition the group and then show that given by is a bijection. Then conclude that where is the number of cosets formed by .

With equal ease show that is a group (looking at it like that is even easier). If this group were to have a group it would have to be a divisor of and thus is either ...but since the subgroup a non-trivial (assumed proper) it must be ...finish it.Show that the set G = {1,-1,i,-i} (i - (sqrt of -1))

forms a group with respect to multiplication of complex numbers.Obtain a non trivial subgroup h, justifying your choice and use it to illustrate Lagranges Theorem