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Title: Broué's conjecture for finite groups
Author: Sannella, Stefano
ISNI:       0000 0004 7432 3419
Awarding Body: University of Birmingham
Current Institution: University of Birmingham
Date of Award: 2018
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This research project consists of using the theory of perverse equivalences to study Broue's abelian defect group conjecture for the principal block of some finite groups when the defect group is elementary abelian of rank 2. We will look at G=\Omega^{ +} 8(2} and prove the conjecture in characteristic 5, the only open case for this group. We will also look at which result the application of our algorithm leads when G= { }^2F 4(2}'.2, {}^3D_ 4(2}, Sp_8(2}; for those groups, it seems that a slight modification of our method is required to complete the proof of the conjecture. Finally, we will see what happens when we apply our method -which is mainly used for groups G of Lie type- to some sporadic groups, namely G=j_2, He, Suz, Fi_{22}.
Supervisor: Not available Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral
EThOS ID:  DOI: Not available
Keywords: QA Mathematics