A result extended from groups to Hopf algebras (Q1375771)

We work over an algebraically closed field \(k\) of characteristic 0. The aim of this short note is to prove the following theorem, which is an extension of a well-known fact on finite groups to finite-dimensional semisimple Hopf algebras. Theorem. Let \(p\) be an odd prime which is congruent to 2 modulo 3. Then a semisimple Hopf algebra of dimension \(3p\) is isomorphic to the group-like Hopf algebra \(kC_{3p}\) of the cyclic group \(C_{3p}\) of order \(3p\).