Abstract
We study several families of semisimple Hopf algebras, arising as bismash products, which are constructed from finite groups with a certain specified factorization. First we associate a bismash product H q of dimension q ( q − 1 ) ( q + 1 ) to each of the finite groups PGL 2 ( q ) and show that these H q do not have the structure (as algebras) of group algebras (except when q = 2 , 3 ). As a corollary, all Hopf algebras constructed from them by a comultiplication twist also have this property and are thus non-trivial. We also show that bismash products constructed from Frobenius groups do have the structure (as algebras) of group algebras.
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