Integral group ring of Rudvalis simple group. (English) Zbl 1209.16027

Bovdi, V. A.; Konovalov, A. B.

Ukr. Mat. Zh. 61, No. 1, 1-13 (2009) and Ukr. Math. J. 61, No. 1, 3-13 (2009).

Summary: Using the Luthar-Passi method, we investigate the classical Zassenhaus conjecture for the normalized unit group of the integral group ring of the Rudvalis sporadic simple group \(Ru\). As a consequence, for this group we confirm the Kimmerle conjecture on prime graphs.

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
20D08	Simple groups: sporadic groups

Keywords:

integral group rings; Rudvalis simple group; prime graphs; Luthar-Passi method; Zassenhaus conjecture; Kimmerle conjecture; torsion units; finite simple groups

Software:

LAGUNA; GAP