Torsion units in the integral group ring of the alternating group of degree 6. (English) Zbl 1161.16023

Motivated by a conjecture of H. Zassenhaus and a conjecture of W. Kimmerle, the author studies the orders and partial augmentations of torsion units in the integral group ring of the alternating group of degree \(6\). Some of the torsion units are shown to be rationally conjugate to an element of the base group, whereas for others it is proved that their partial augmentations are bounded by \(-2\) and \(2\).


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


Full Text: DOI


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