The Brauer indecomposability of Scott modules with wreathed $2$-group vertices
| Autor: | İpek Tuvay, Shigeo Koshitani |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Finite group
General Mathematics 20C20 20C05 Mathematics::Rings and Algebras Group Theory (math.GR) Indecomposability Prime (order theory) Combinatorics FOS: Mathematics Bimodule Order (group theory) Representation Theory (math.RT) Abelian group 2-group Indecomposable module Mathematics::Representation Theory Mathematics - Group Theory Mathematics - Representation Theory Mathematics |
| Popis: | We give a sufficient condition for the $kG$-Scott module with vertex $P$ to remain indecomposable under taking 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 wreathed $2$-subgroup of a finite group $G$. This generalizes results for the cases where $P$ is abelian and some others. The motivation of this paper is 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 that then can possibly lift to a splendid derived equivalence. |
| Databáze: | OpenAIRE |
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