A research on symbolic and algebraic computation of groups and combinatorics and its application

在前人的研究中，我利用关联方案的自同构群来加速传递群的规范化计算。相干构形的自同构群与置换群的正则化器有关，而置换群可能不是传递的。这一次，我将它们应用于加速归一化器的计算和检验置换群的子群的共轭性，这些子群可能不是传递的。双传递群形成了与对称群相同的平凡关联方案。置换群对点的t元组的作用形成了t超格式。一个t-上格式由k= 1,2，…点集合的k元组的分区组成。它满足一定的条件。双传递群在不同的2元组点上形成只有一个划分的3-超方案。利用计算机构造了这类大小适中但不是由双传递群构成的3-超方案，并作为应用，从一些方案中得到了2-设计。

In a previous research I applyed automorphism groups of association schemes to speed up the computation of normalizers of transitive groups. Automorphism groups of coherent configurations are related to the normalizers of permutation groups which may not be transitive. This time, I applied them to speed up the computation of normalizers and testing conjugacy of subgroups of permutation groups which may not be transitive.Doubly transitive groups form a trivial association scheme same as those formed by symmetric groups. The action of a permutation group on t-tuples of points forms t-superscheme. A t-superscheme consists of partitions of k-tuples of a set of points for k=1, 2,.., t satisfying certain conditions. Doubly transitive groups form 3-superschemes with only one partition on distinct 2-tuples of points. Using computers, we constructed such 3-superschems of moderate size but not formed by doubly transitive groups and, as an application, obtained 2-designs from some of the schemes.