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Embeddings of Ree unitals in a projective plane over a field
Finite Fields and Their Applications ( IF 1 ) Pub Date : 2021-05-18 , DOI: 10.1016/j.ffa.2021.101875 Gábor P. Nagy
中文翻译:
Ree单元的嵌入在一个域上的投影平面上
更新日期:2021-05-18
Finite Fields and Their Applications ( IF 1 ) Pub Date : 2021-05-18 , DOI: 10.1016/j.ffa.2021.101875 Gábor P. Nagy
We show that the Ree unital has an embedding in a projective plane over a field F if and only if and is a subfield of F. In this case, the embedding is unique up to projective linear transformations. Besides elementary calculations, our proof uses the classification of the maximal subgroups of the simple Ree groups.
中文翻译:
Ree单元的嵌入在一个域上的投影平面上
我们证明里 仅当且仅当在场F上的投影平面中有嵌入 和 是F的子字段。在这种情况下,嵌入在投影线性变换之前都是唯一的。除了基本计算之外,我们的证明还使用了简单Ree群的最大子群的分类。