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

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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.