Abstract
We give a sufficient condition for the -Scott module with vertex to remain indecomposable under taking the Brauer construction for any subgroup of as -module, where is a field of characteristic , and is a wreathed -subgroup of a finite group . This generalizes results for the cases where is abelian and some others. The motivation of this paper is that the Brauer indecomposability of a -permutation bimodule ( is a prime) is one of the key steps in order to obtain a splendid stable equivalence of Morita type by making use of the gluing method that then can possibly lift to a splendid derived equivalence.
Citation
Shigeo Koshitani. İpek Tuvay. "The Brauer indecomposability of Scott modules with wreathed -group vertices." Rocky Mountain J. Math. 51 (4) 1259 - 1280, August 2021. https://doi.org/10.1216/rmj.2021.51.1259
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