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- W122669563 abstract "Since all finite simple groups have been classified [], it is a natural question whether the major conjectures in modular representation theory are consequences of this important and deep classification theorem. In this article, a survey is given about the progress which has been achieved on the famous open conjectures of J. Alperin [] and R. Brauer [] during the last decade. It turns out that all these problems have rather complete affirmative answers for almost all infinite series of finite groups like the symmetric, classical or exceptional groups of Lie type G for which there is a good parametrization of the irreducible characters χ of G into p-blocks B, where p is a prime divisor of the order of G. Using techniques from Clifford theory as described in Berger [] and chapter 10 of Feit [] it is often possible to reduce the proof of a general conjecture to the case of the automorphism groups of all the covering groups of a finite simple group. In particular, such reduction theorems exist for one direction of Brauer’s height zero conjecture and for Alperin’s weight conjecture as has been shown by Berger and Knörr [] and Dade [], respectively." @default.
- W122669563 created "2016-06-24" @default.
- W122669563 creator A5005160731 @default.
- W122669563 date "1991-01-01" @default.
- W122669563 modified "2023-09-27" @default.
- W122669563 title "Contributions to Modular Representation Theory of Finite Groups" @default.
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- W122669563 doi "https://doi.org/10.1007/978-3-0348-8658-1_5" @default.
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