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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.)
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