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

在以前的研究中，我应用结合模式的自同构群来加速传递群的正规化子的计算。相干组态的自同构群与置换群的正规化子有关，而置换群的正规化子不一定是传递的。这一次，我应用它们来加速正规化子的计算和检验置换群的子群的共轭性，这些置换群可能是不传递的，双传递群形成了与对称群相同的平凡结合方案。置换群在点的t-元组上的作用形成t-超方案。一个t-超方案由一组点的k-元组的划分组成，k=1，2，..，t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。本文利用计算机构造了这类非双传递群构成的中等大小的3-超样，作为应用，从某些方案中得到了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.