On semisimple Hopf algebras of dimension $2q^3$

Abstract

Let $q$ be a prime number, $k$ an algebraically closed field of characteristic 0, and $H$ a semisimple Hopf algebra of dimension $2q^3$. This paper proves that $H$ is always semisolvable. That is, such Hopf algebras can be obtained by (a number of) extensions from group algebras or duals of group algebras.

The title has been changed, and some minor typos have been corrected. arXiv admin note: substantial text overlap with arXiv:1105.4398; and text overlap with arXiv:math/0305038 by other authors

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