对称群S_5的所有幂零子群和可解子群

All Nilpotent Subgroups and Solvable Subgroups of Symmetric Group S_5

给出了S5的全部102个幂零子群和154个可解子群,其中幂零子群分为10个共轭类,可解子群分为17个共轭类,而且给出了每个子群的阶和一个最小生成元组.

This paper gives all die nilpotent subgroups and solvable subgroups of symmetric group S5. There are 102 nilpotent subgroups which belongs to 10 conjugacy classes and 154 solvable subgroups which belongs to 17 conjugacy classes. The generators and order of each subgroup are given.