缺陷群为铃木 2 群的嵌块

Pub Date : 2024-10-21 DOI:10.1016/j.jalgebra.2024.10.011
Charles W. Eaton
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引用次数: 0

摘要

我们对缺陷群为铃木 2 群的所有图块进行了莫里塔等价分类。这种分类既适用于在合适的离散估值环上的组块,也适用于在代数闭域上的组块,而且事实上直到基本的莫里塔等价性都成立。因此,多诺万猜想对铃木 2 群成立。证明的一个推论是,有限群的铃木 Sylow 2 子群没有非奇数阶正则子群,是琐细交集。
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Blocks whose defect groups are Suzuki 2-groups
We classify up to Morita equivalence all blocks whose defect groups are Suzuki 2-groups. The classification holds for blocks over a suitable discrete valuation ring as well as for those over an algebraically closed field, and in fact holds up to basic Morita equivalence. As a consequence Donovan's conjecture holds for Suzuki 2-groups. A corollary of the proof is that Suzuki Sylow 2-subgroups of finite groups with no nontrivial odd order normal subgroup are trivial intersection.
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