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https://doi.org/10.1007/978-3-319-62057-2The arguments here are quite condensed and use a fair amount of integral representation theory. Since it is essential only to construct counter examples, it can be skipped by the unfamiliar reader.

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IntroductionThe results and arguments in the sections on the isomorphism problem are due to Leonard Scott in collaboration with K. W. Roggenkamp in the last ten years unless otherwise stated..

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The leading coefficient of unitsThe aim in this section is to prove the following...... ∈ . |G| .(1) = 0 . = .(1), .(1) .1 . {Equ1 page 15}..(1) = 0.

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Zassenhaus conjectureZassenhaus conjectured in [Se; 83] that group bases in . are not only isomorphic, they are even conjugate in the group ring .. Here we view .. This would have far reaching consequences. For example for the automorphism group of . this implies immediately that every normalized automorphism is central up to a group automorphism of the group base ..