An improvement of a function computing normalizers for permutation groups

Abstract

Computation of normalizers for permutation groups is sometimes very hard even if the degrees are small. The author previously obtained some methods to compute normalizers of permutation groups and wrote programs implementing the methods. The programs were mainly applied to groups of small degree such as transitive groups of degree up to 30 in the GAP library. The author will tune up the implementation to speed up the computation of normalizers of permutation groups and apply it to permutation groups of degree up to 100. In our experiments, the normalizers of the primitive groups up to degree 100 and their stabilizers of one point in the symmetric groups are computed. © 2010 Springer-Verlag.