实现某些Todd模块的融合系统

Pub Date : 2022-04-16 DOI:10.1515/jgth-2022-0074

B. Oliver

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引用次数: 2

摘要

摘要研究了一类有限3群上的简单融合系统，这些系统涉及Mathieu群的Todd模2 ^ m12 2M_{12}， m11 M_{11}，以及a6 = o2 ^ (m10) A_{6}=O^{2}(M_{10})在f3 \mathbb{F}_{3}上的3融合系统，并证明了它们都是几乎简单群的3融合系统同构的。作为结果之一，我们给出了康威散散单群的新的三局部刻画。

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Fusion systems realizing certain Todd modules

Abstract We study a certain family of simple fusion systems over finite 3-groups, ones that involve Todd modules of the Mathieu groups 2 ⁢ M 12 2M_{12} , M 11 M_{11} , and A 6 = O 2 ⁢ ( M 10 ) A_{6}=O^{2}(M_{10}) over F 3 \mathbb{F}_{3} , and show that they are all isomorphic to the 3-fusion systems of almost simple groups. As one consequence, we give new 3-local characterizations of Conway’s sporadic simple groups.

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