2-blocks with abelian defect groups
2-blocks with abelian defect groups
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DOI：
10.1016/j.aim.2013.12.024
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发表时间：
2013-05
影响因子：
1.7
通讯作者：
Charles W. Eaton;R. Kessar;B. Kulshammer;Benjamin Sambale
中科院分区：
文献类型：
--
作者：
Charles W. Eaton;R. Kessar;B. Kulshammer;Benjamin Sambale
本文给出了具有交换亏群的2-块拟单群的一个分类，直到Morita等价。结果证明了Donovan猜想对初等交换2-群成立，并且证明了任意交换2-群的Cartan矩阵的元素是有界的.我们还证明了一个亏群为C2 m× C2 m（m ≠ 2）的块具有两个Morita等价类型之一，因此它与亏群正规化子的Brauer对应块是Morita等价的.这就完成了对秩为2的阿贝尔亏群的2-块的Morita等价型的分析，由此我们得出Donovan猜想对这类2-群成立的结论。进一步的应用是完成的确定的数量不可约字符块的阿贝尔缺陷群的顺序16。证明使用有限单群的分类。
We give a classification, up to Morita equivalence, of 2-blocks of quasi-simple groups with abelian defect groups. As a consequence, we show that Donovanʼs conjecture holds for elementary abelian 2-groups, and that the entries of the Cartan matrices are bounded in terms of the defect for arbitrary abelian 2-groups. We also show that a block with defect groups of the form C 2 m× C 2 m for m⩾ 2 has one of two Morita equivalence types and hence is Morita equivalent to the Brauer correspondent block of the normaliser of a defect group. This completes the analysis of the Morita equivalence types of 2-blocks with abelian defect groups of rank 2, from which we conclude that Donovanʼs conjecture holds for such 2-groups. A further application is the completion of the determination of the number of irreducible characters in a block with abelian defect groups of order 16. The proof uses the classification of finite simple groups.