一种生成对称群S9所有Sylow-p子群的算法

根据对称群的基本性质以及第二同构定理，给出了通过添加生成元到P群来构造对称群的一个Sylow-p子群的定理，添加的生成元保证能够快速得到对称群的一个Sylow—p子群．根据第二西洛定理求出了所有共轭子群，即所有Sylow-p子群．针对求所有共轭子群过程中面临共轭子群出现重复的问题，利用正规化子的性质，找到使得两个Sylow-p子群共轭的元，保证每次求的Sylow-P子群不重复．将此算法应用于S1，实验表明该算法可操作性强，耗费时间少．

Algorithm Generating a Sylow-p Subgroups of the Group S9

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.