Broue's Abelian Defect Group Conjecture for the Tits Group

Abstract

In this paper we prove that Broue's abelian defect group conjecture holds for the Tits group ${}^2{F}_4(2{)}^{\prime }$. Also we prove that under certain conditions we are able to lift derived equivalences and use this to prove Broue's conjecture for the group ${}^2{F}_4(2)$.

23 pages