Algorithm Generating a Sylow-p Subgroups of the Group S_9
Wenchao Hu · Journal of Wuhan University · 2006
Based on the second isomorphic theorem and properties of the symmetric group,a theorem is proposed to construct one Sylow-p group of symmetric group by adding generators to p-group.The additive generators we choose can ensure to obtain Sylow-p subgroup quickly.And then all the conjugate subgroups can be derived.The properties of normalizers is adopted to find an element that persuade one Sylow-p subgroup conjugates to another,and this can avoid redundancy checking.When applying to S_9,experiments show that this algorithm enjoys both easy implementation and low time complexity.