I. Show that if A is a finite abelian group, then
any homomorphism  g: A --> GL(n,C) is conjugate in GL(n,C) to
h: A --> (GL(1,C))^n --> GL(n,C) .

II. Let SU(n) be the subset of GL(n,C) consisting of matrices
    $T$ such that (1) det( $T$) = 1  and 
                  (2) T * (conjugate)(transpose)T = Id_n
    (a) Show that SU(n) is closed under taking products and inverses
        and hence is a subgroup of GL(n,C).
    (b) Let $g$ be an element of SU(n) and $k$ a positive integer.
        Show that that exists an $h$ in $SU(n) such that
        $h^k$ = $g$. 
III. Let $D_{2n}$ be the dihedral group of order $2n$ and $Q_{2n}$
     be the quaternion group of order $Q_{2n}$. Describe the irreducible
     representations of each. You can restrict yourself to n=2,3, and 4.