Some classes of semisimple group (and loop) algebras over finite fields

We determine the structure of the semisimple group algebra of certain groups over the rationals and over those finite fields where the Wedderburn decompositions have the least number of simple components We apply our work to obtain similar information about the loop algebras of mdecomposable RA loops and to produce negative answers to the isomorphism problem over various fields (C) 2010 Elsevier Inc All rights reservedNatural Sciences and Engineering Research Council of CanadaNatural Sciences and Engineering Research Council of CanadaFAPESP[2004/15319 3]Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)FAPESP[2008/57553 3]CNPq of Brazil[300243/79 0]Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq