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Keywords:
Zassenhaus conjecture; torsion unit; partial augmentation; integral group ring
Zassenhaus conjecture; torsion unit; partial augmentation; integral group ring
Summary:
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 $\rm PSL(2,11)$. Additionally we prove that the Prime graph question is true for the automorphism group of the simple group $\rm PSL(2,13)$.
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