Computing Sylow Subgroups in Permutation Groups

Abstract We describe the theory and implementation of a practical algorithm for computing a Sylow subgroup of a permutation group and for finding an element that conjugates one Sylow subgroup to another. The performance of the current implementations in the Magma system represents a significant improvement on previous implementations for many important classes of examples and generally extends the range of realistic applicability to groups of much larger degrees than before.

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