Another counterexample to a conjecture of Zassenhaus, Beiträge Algebra Geom

Abstract. A metabelian group G of order 1440 is constructed which provides a counterexample to a conjecture of Zassenhaus on automorphisms of integral group rings. The group is constructed in the spirit of [8]. An augmented automorphism of ZG which has no Zassenhaus factorization is given explicitly (this was already done in [7] for a group of order 6720), but this time only a few distinguished group ring elements are used for its construction, carefully exploiting certain congruence relations satisfied by powers of these elements. 1