## The prime graph conjecture for integral group rings of some alternating groups.(English)Zbl 1301.16045

Summary: We investigate the classical H. Zassenhaus conjecture for integral group rings of alternating groups $$A_9$$ and $$A_{10}$$ of degree 9 and 10, respectively. As a consequence of our previous results we confirm the Prime Graph Conjecture for integral group rings of $$A_n$$ for all $$n\leq 10$$.

### 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 05C25 Graphs and abstract algebra (groups, rings, fields, etc.)