Broue's Abelian Defect Group Conjecture for the Tits Group

TL;DR

This paper proves Broue's abelian defect group conjecture for the Tits group and extends the result to the group $^2F_4(2)$ by lifting derived equivalences under certain conditions.

Contribution

The paper establishes Broue's conjecture for the Tits group and demonstrates a method to lift derived equivalences to prove the conjecture for related groups.

Findings

Broue's conjecture holds for the Tits group $^2F_4(2)'$.

Derived equivalences can be lifted under certain conditions.

Broue's conjecture is verified for the group $^2F_4(2)$.

Abstract

In this paper we prove that Broue's abelian defect group conjecture holds for the Tits group $^2F_4(2)'$. 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 $^2F_4(2)$.