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