On saturated fusion systems and Brauerindecomposability of Scott modules
On saturated fusion systems and Brauerindecomposability of Scott modules
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关于饱和融合系统和 Scott 模的 Braue 可分解性
DOI：
10.1016/j.jalgebra.2011.04.029
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发表时间：
2011
期刊：
影响因子：
--
通讯作者：
N.Mitsuhashi
中科院分区：
文献类型：
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作者：
R.Kessar;N. Kunugi;N.Mitsuhashi
设p是素数，G是有限群，P是G的p-子群，k是特征p的代数闭域.我们研究范畴F P(G)与具有顶点P的p-置换Kg-模在Brauer构造下的性质的关系.给出了F-P(G)为饱和融合系统的一个充分条件。证明了对于具有交换顶点的Scott模，我们的条件也是必要的。为了得到我们的结果，我们给出了由Alperin-Broué和Broué-Puig意义下的(b，G)-Brauer对数据产生的范畴是基础p-群上的饱和融合系统的一个判据。
Let p be a prime number, G a finite group, P a p-subgroup of G and k an algebraically closed field of characteristic p. We study the relationship between the category F P (G) and the behavior of p-permutation kG-modules with vertex P under the Brauer construction. We give a sufficient condition for F P (G) to be a saturated fusion system. We prove that for Scott modules with abelian vertex, our condition is also necessary. In order to obtain our results, we give a criterion for the categories arising from the data of (b, G)-Brauer pairs in the sense of Alperin–Broué and Broué–Puig to be saturated fusion systems on the underlying p-group.