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arXiv · 1804.08158

An observation on the module structure of block algebras

Matthew Gelvin
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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 invariant 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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Matthew Gelvin. 2018-04-22. An observation on the module structure of block algebras. https://arxiv.org/abs/1804.08158

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