Abstract. In this paper, we investigate the Zassenhaus conjecture for exceptional groups of Lie type $G_2(q)$ for $q=\{3,4\}$. Consequently, we prove that the Prime graph question is true for these groups.

DOI: 10.14232/actasm-015-048-6

AMS Subject Classification (1991): 16S34, 20C05

Keyword(s): Zassenhaus Conjecture, torsion unit, partial augmentation, integral group ring

Received July 1, 2015, and in revised form November 2, 2015. (Registered under 48/2015.)