Zassenhaus conjecture for \(A_5\). (English) Zbl 0678.16008

The authors show that whether two torsion units in the integral group ring \(\mathbb{Z} G\) of a finite group \(G\) are rationally conjugate can be read from the partial augmentations of their powers. This is applied to the alternating group on five letters \(A_5\) and yields that, up to rational conjugation, all torsion units already belong to \(A_5\).
Reviewer: J.Ritter


16U60 Units, groups of units (associative rings and algebras)
16S34 Group rings
20C05 Group rings of finite groups and their modules (group-theoretic aspects)
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