Broué's conjecture for non-principal 3-blocks of finite groups |
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Authors: | Shigeo Koshitani Naoko Kunugi |
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Affiliation: | a Department of Mathematics, Faculty of Science, Chiba University, Yayoi-cho, Inage-Ku, Chiba-shi 263-8522, Japan b Department of Mathematics, Faculty of Science, Ochanomizu University, Bunkyo-ku, Tokyo 112-8610, Japan c Department of Mathematical System Science, Faculty of Science and Technology, Hirosaki University, Hirosaki 036-8561, Japan |
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Abstract: | In representation theory of finite groups, there is a well-known and important conjecture due to M. Broué. He conjectures that, for any prime p, if a p-block A of a finite group G has an abelian defect group D, then A and its Brauer correspondent p-block B of NG(D) are derived equivalent. We demonstrate in this paper that Broué's conjecture holds for two non-principal 3-blocks A with elementary abelian defect group D of order 9 of the O'Nan simple group and the Higman-Sims simple group. Moreover, we determine these two non-principal block algebras over a splitting field of characteristic 3 up to Morita equivalence. |
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Keywords: | 20C20 20C34 20C05 |
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