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

Salim, Mohamed A.

Int. J. Group Theory 2, No. 1, 175-185 (2013).

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.)

Keywords:

integral group rings; Zassenhaus conjecture; prime graph conjecture; torsion units; alternating groups; groups of units