An observation on the module structure of block algebras |
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Authors: | Matthew J K Gelvin |
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Institution: | 1. Department of Mathematics, Bilkent University, Ankara, Turkeymatthew.gelvin@bilkent.edu.tr |
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Abstract: | Let B be a p-block of the finite group G. We observe that the p-fusion of G constrains the module structure of B: Any basis of B that is closed under the left and right multiplications of a chosen Sylow p-subgroup S of G must in fact form a semicharacteristic biset for the fusion system on S induced by G. The parameterization of such semicharacteristic bisets can then be applied to relate the module structure and defect theory of B. |
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Keywords: | Blocks of finite groups characteristic bisets fusion systems |
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