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

Salim, Mohamed A. M.

Acta Math. Acad. Paedagog. Nyházi. (N.S.) 27, No. 1, 9-22 (2011).

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

Keywords:

Zassenhaus conjecture; Kimmerle conjecture; torsion units; integral group rings; alternating group \(A_7\); alternating group \(A_8\); groups of units