论文标题
与给定层维度的关联方案：在彼得·诺伊曼的纸上
Association schemes with given stratum dimensions: on a paper of Peter M. Neumann
论文作者
论文摘要
1969年1月，彼得·诺伊曼（Peter M.主要定理对原始的限制限制了原始的参数，但不是2次限制度的限制。该论文从未发表过，结果取决于有限简单组的分类，例如对原始奇数群的分类，取代了更强的定理。 但是，还有进一步的原因对本文感兴趣。首先，它是在将组合技术引入有限置换组的时候写的，并且本文提供了这些技术的很好的摘要和应用。其次，就像赫尔穆特·维兰特（Helmut Wielandt）在原始2p的原始组上一样，它可以重新解释为结合方案的组合结果，其共同的特征性方案具有相当有限的形式。该结果既不使用P的原始性，也不使用与组合结构相关的排列组的存在。我们提取这些结果并提供相关组合学的详细信息。
In January 1969, Peter M. Neumann wrote a paper entitled "Primitive permutation groups of degree 3p". The main theorem placed restrictions on the parameters of a primitive but not 2-transitive permutation group of degree three times a prime. The paper was never published, and the results have been superseded by stronger theorems depending on the classification of the finite simple groups, for example a classification of primitive groups of odd degree. However, there are further reasons for being interested in this paper. First, it was written at a time when combinatorial techniques were being introduced into the theory of finite permutation groups, and the paper gives a very good summary and application of these techniques. Second, like its predecessor by Helmut Wielandt on primitive groups of degree 2p, it can be re-interpreted as a combinatorial result concerning association schemes whose common eigenspaces have dimensions of a rather limited form. This result uses neither the primality of p nor the existence of a permutation group related to the combinatorial structure. We extract these results and give details of the related combinatorics.
