## Kimmerle’s conjecture for integral group rings of some alternating groups.(English)Zbl 1240.16047

Summary: 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 Kimmerle’s conjecture about prime graphs for those groups.

### MSC:

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