Torsion units in integral group rings of metacyclic groups (Q801143)

The paper contains the first non-trivial result in connection with a striking conjecture going back to Zassenhaus and stating that to each unit of finite order in the integral group ring \({\mathbb{Z}}G\) of a finite group G there exists a group element which, up to a sign, in the rational group algebra \({\mathbb{Q}}G\) is conjugate to the unit in question. The conjecture is confirmed for G being a split extension of a cyclic p-group by a cyclic p'-group with faithful action. Meanwhile it has also been confirmed for less special metacyclic groups [the second author and the reviewer, Math. Ann. 264, 257-270 (1983; Zbl 0521.16006)].