The Conway-Norton algebras for ?(6,3), ?(7,3), F'24, and their full automorphism groups.
Let be a finite group. The main supergraph is a graph with vertex set in which two vertices and are adjacent if and only if or . In this paper, we will show that if and only if . As a main consequence of our result we conclude that Thompson’s problem is true for the small Ree group .
We investigate the Zassenhaus conjecture regarding rational conjugacy of torsion units in integral group rings for certain automorphism groups of simple groups. Recently, many new restrictions on partial augmentations for torsion units of integral group rings have improved the effectiveness of the Luther-Passi method for verifying the Zassenhaus conjecture for certain groups. We prove that the Zassenhaus conjecture is true for the automorphism group of the simple group . Additionally we prove that...