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Let k be an algebraically closed field of prime characteristic p, and let P be a p-subgroup of a finite group G. We give sufficient conditions for the kG-Scott module Sc(G,P) with vertex P to remain indecomposable under the Brauer construction with respect to any subgroup of P. This generalizes similar results for the case where P is abelian. The background motivation for this note is the fact that the Brauer indecomposability of a p-permutation bimodule is a key step towards showing that the module under consideration induces a stable equivalence of Morita type, which then may possibly be lifted to a derived equivalence.
|Additional Information:||This is a pre-copyedited, author-produced PDF of an article accepted for publication in Quarterly Journal of Mathematics following peer review. The version of record Kessar, R., Koshitani, S. & Linckelmann, M. (2015). On the Brauer Indecomposability of Scott Modules. The Quarterly Journal of Mathematics, 66(3), pp. 895-903. doi: 10.1093/qmath/hav010 is available online at: http://qjmath.oxfordjournals.org/content/66/3/895.|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||School of Engineering & Mathematical Sciences > Department of Mathematical Science|
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