Broué's conjecture for finite groups
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 charac...
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ndltd-bl.uk-oai-ethos.bl.uk-7603512019-04-03T06:29:20ZBroué's conjecture for finite groupsSannella, Stefano2018This 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}.510QA MathematicsUniversity of Birminghamhttps://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.760351http://etheses.bham.ac.uk//id/eprint/8462/Electronic Thesis or Dissertation |
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510 QA Mathematics Sannella, Stefano Broué's conjecture for finite groups |
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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}. |
author |
Sannella, Stefano |
author_facet |
Sannella, Stefano |
author_sort |
Sannella, Stefano |
title |
Broué's conjecture for finite groups |
title_short |
Broué's conjecture for finite groups |
title_full |
Broué's conjecture for finite groups |
title_fullStr |
Broué's conjecture for finite groups |
title_full_unstemmed |
Broué's conjecture for finite groups |
title_sort |
broué's conjecture for finite groups |
publisher |
University of Birmingham |
publishDate |
2018 |
url |
https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.760351 |
work_keys_str_mv |
AT sannellastefano brouesconjectureforfinitegroups |
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1719013125393481728 |