Abstract
We develop a mechanism for classication of isomor- phism types of non-trivial semisimple Hopf algebras whose group of grouplikes G(H) is abelian of prime index p which is the small- est prime divisor of |G(H)|. We describe structure of the second cohomology group of extensions of kCp by k G where Cp is a cyclic group of order p and G a finite abelian group. We carry out an explicit classification for Hopf algebras of this kind of dimension p 4 for any odd prime p. The ground field is algebraically closed of characteristic 0.
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