论文标题
Scott模块的Brauer不可塑性，带花圈$ 2 $ - 组顶点
The Brauer indecomposability of Scott modules with wreathed $2$-group vertices
论文作者
论文摘要
我们为带顶点$ p $的$ kg $ -scott模块提供了足够的条件，以保持不可塑性，以在任何子组$ q $ of $ p $ as as $ k [q \，c_g（q）$ - 模块中，$ k $ a $ k $是特征性$ 2 $ 2 $ 2 $ $ p $ $ $ $ $ $ $ a的$ a $ a $ a a $ a a $ a $ a $ a $ a $ a $对于$ P $是Abelian和其他一些情况的情况，这将概括结果。本文的动机是，$ p $ - permoutt的bimodule（$ p $是一个典型）的不可分解性是一个关键步骤之一，以通过利用粘合方法来获得出色的稳定等效性，然后利用粘合方法，然后可以将其提升到出色的衍生等价。
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.
