Hopf algebras of dimension 2p

Let H be a finite-dimensional Hopf algebra over an algebraically closed field of characteristic 0. If H is not semisimple and dim(H) = 2n for some odd integer n, then H or H* is not unimodular. Using this result, we prove that if dim(H) = 2p for some odd prime p, then H is semisimple. This completes the classification of Hopf algebras of dimension 2p.