Kimmerle's conjecture for integral group rings of some alternating groups

Abstract: Using the Luthar-Passi method and results of Hertweck, we study the long-standing conjecture of Zassenhaus for integral group rings of alternating groups $A_{n}$, $n\leq 8$. As a consequence of our results, we confirm the Kimmerle's conjecture about prime graphs for those groups.

Keywords: Zassenhaus conjecture, Kimmerle conjecture, torsion unit, integral group ring

Classification (MSC2000): 16S34; 20C05, 20D08

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