Controlled blocks of the finite quasisimple groups for odd primes |
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Authors: | Jianbei An |
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Affiliation: | Department of Mathematics, University of Auckland, Auckland, New Zealand |
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Abstract: | We classify controlled blocks, introduced by Alperin and Broué in 1979 for all quasisimple groups G for odd primes. The results imply that every nilpotent block of G has abelian defect groups, which in turn is one of the main results proved in An and Eaton (2011) [6]. We also give an explicit characterization of non-controlled blocks of all quasisimple groups G for odd primes. This implies the block theoretic analogue of Glauberman?s ZJ-theorem for G proved by Kessar, Linckelmann and Robinson (2002) [18]. |
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Keywords: | Modular representations of finite groups Controlled blocks Quasisimple groups |
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