## 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

### MSC:

 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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### References:

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