# 置换群

## 常见的置换群

### ${\displaystyle M=\{1,2\))$

${\displaystyle (1),(1\ 2)}$

### ${\displaystyle M=\{1,2,3\))$

${\displaystyle (1),(1\ 2),(1\ 3),(2\ 3),(1\ 2\ 3),(1\ 3\ 2)}$

### ${\displaystyle M=\{1,2,3,4\))$

${\displaystyle (1),}$ ${\displaystyle (1\ 2),(1\ 3),(1\ 4),(2\ 3),(2\ 4),(3\ 4),}$ ${\displaystyle (1\ 2\ 3),(1\ 3\ 2),(1\ 2\ 4),(1\ 4\ 2),(1\ 3\ 4),(1\ 4\ 3),(2\ 3\ 4),(2\ 4\ 3),}$ ${\displaystyle (1\ 2\ 3\ 4),(1\ 2\ 4\ 3),(1\ 3\ 2\ 4),(1\ 3\ 4\ 2),(1\ 4\ 2\ 3),(1\ 4\ 3\ 2),(1\ 2)(3\ 4),(1\ 3)(2\ 4),(1\ 4)(2\ 3)}$

## 参考

• John D. Dixon and Brian Mortimer. Permutation Groups. Number 163 in Graduate Texts in Mathematics. Springer-Verlag, 1996.
• Akos Seress. Permutation group algorithms. Cambridge Tracts in Mathematics, 152. Cambridge University Press, Cambridge, 2003.
• Meenaxi Bhattacharjee, Dugald Macpherson, Rögnvaldur G. Möller and Peter M. Neumann. Notes on Infinite Permutation Groups. Number 1698 in Lecture Notes in Mathematics. Springer-Verlag, 1998.
• Alexander Hulpke. GAP Data Library "Transitive Permutation Groups".