An observation on the module structure of block algebras
Date
2019-05-26
Authors
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Source Title
Communications in Algebra
Print ISSN
0092-7872
Electronic ISSN
1532-4125
Publisher
Taylor & Francis
Volume
47
Issue
12
Pages
5286 - 5293
Language
English
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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.