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Isomorphisms of Modular Group Algebras: An Algorithm and its Application to Groups of Order

Abstract We shall describe an algorithm based on an idea of Roggenkamp and Scott (Roggenkamp and Scott, 1993) ) to compute Hom alg ( F H, F G), where H, G are finite p -groups and F H, F G are their group algebras over F = Z / p Z . Using this algorithm it is possible to determine whether two such group algebras are isomorphic. An implementation of the algorithm has been used to show that the groups of order 64 are determined by their modular group algebras over Z /2 Z .