The Brauer indecomposability of Scott modules with semidihedral vertex
| Autor: | Koshitani, Shigeo, Tuvay, İpek |
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| Rok vydání: | 2019 |
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| Druh dokumentu: | Working Paper |
| DOI: | 10.1017/S0013091521000067 |
| Popis: | We present a sufficient condition for the $kG$-Scott module with vertex $P$ to remain indecomposable under the Brauer construction for any subgroup $Q$ of $P$ as $k[Q\,C_G(Q)]$-module, where $k$ is a field of characteristic $2$, and $P$ is a semidihedral $2$-subgroup of a finite group $G$. This generalizes results for the cases where $P$ is abelian or dihedral. The Brauer indecomposability is defined \linebreak by R.~Kessar, N.~Kunugi and N.~Mitsuhashi. The motivation of \linebreak this paper is a fact that the Brauer indecomposability of a $p$-permutation bimodule ($p$ 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 due to Brou\'e, Rickard, Linckelmann and Rouquier, that then can possibly be lifted to a splendid derived (splendid Morita) equivalence. Comment: 10 pages |
| Databáze: | arXiv |
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