Computing normalizers of permutation groups efficiently using isomorphisms of association schemes
ISSAC '00 Proceedings of the 2000 international symposium on Symbolic and algebraic computation
Computing isomorphisms of association schemes and its application
Journal of Symbolic Computation - Special issue on computer algebra and mechanized reasoning: selected St. Andrews' ISSAC/Calculemus 2000 contributions
Classification of association schemes of small order
Discrete Mathematics - The 2000 Com2MaC conference on association schemes, codes and designs
Polynomial-time normalizers for permutation groups with restricted composition factors
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
An improvement of a function computing normalizers for permutation groups
ICMS'10 Proceedings of the Third international congress conference on Mathematical software
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In GAP system it takes unreasonably long time to compute the normalizers of some permutation groups, even though they are of small degree. The author gave an algorithm in [7, 8] to compute the normalizers of permutation groups and particularly it worked smoothly for transitive groups of degree up to 22. In 1999 GAP version 4 was released. Since then the GAP system has been improved and in 2004 GAP4r4 had a special function to compute the normalizers in the symmetric groups but it still has difficulties in computing the normalizers of some permutation groups. It has been also found that the author's algorithm in [7, 8] has difficulties in some groups of small degree but larger than 22. So the author will give two new programs improving the computation of normalizers of transitive permutation groups in the symmetric groups. One of them works comparatively smoothly for the transitive groups of degree up to 30.