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Generalized Block Theory

Abstract : This thesis presents a few aspects of the theory of generalized blocks of finite groups. After a short description of the classic and generalized theories, we study the properties of generalized blocks of certain groups. We prove the existence of generalized perfect isometries in three families of groups of Lie rank one, thus generalizing a conjecture of M. Broué. We then study the notion of generalized Cartan group, and a formula is given for the order in the Cartan group of the caracters of the symmetric group. Finally, we define generalized blocks in the finite general linear group, and we show that certain unions of blocks of unipotent caracters satisfy an anologue of the Nakayama Conjecture, as well as an analogue of Brauer's Second Main Theorem.
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Contributor : Jean-Baptiste Gramain <>
Submitted on : Thursday, October 6, 2005 - 6:35:20 PM
Last modification on : Wednesday, July 8, 2020 - 12:43:14 PM
Long-term archiving on: : Friday, April 2, 2010 - 10:57:24 PM


  • HAL Id : tel-00010451, version 1


Jean-Baptiste Gramain. Generalized Block Theory. Mathematics [math]. Université Claude Bernard - Lyon I, 2005. English. ⟨tel-00010451⟩



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