On semisimple Hopf algebras of dimension pq2

We show that if A is a semisimple Hopf algebra of dimension pq(2) over an algebraically closed field k of characteristic zero, then under certain restrictions either A or A* must have a non-trivial central group-like element. We then classify all semisimple Hopf algebras of dimension pq(2) over k which are not simple as Hopf algebras. We also determine all isomorphism classes of Hopf algebras of dimension pgr obtained as abelian extensions. (C) 1999 Academic Press.