代数概論I 置換の計算に使ったやつ（まとめ） - 熊本大学理学部数学コースwiki / 2012年度入学

一つ目「 <(1,2,3,4...,n)>の群」

n=1
(1)

n=2
(1),(1,2)

n=3
(1), (1,2,3), (1,3,2)

n=4
(1), (1,2,3,4), (1,3)(2,4), (1,4,3,2)

n=5
(1), (1,2,3,4,5), (1,3,5,2,4), (1,4,2,5,3), (1,5,4,3,2)

n=6
(1), (1,2,3,4,5,6), (1,3,5)(2,4,6), (1,4)(2,5)(3,6), (1,5,3)(2,6,4), (1,6,5,4,3,2)

n=7
(1), (1,2,3,4,5,6,7), (1,3,5,7,2,4,6), (1,4,7,3,6,2,5), (1,5,2,6,3,7,4), (1,6,4,2,7,5,3), (1,7,6,5,4,3,2)

n=8
(1), (1,2,3,4,5,6,7,8), (1,3,5,7)(2,4,6,8), (1,4,7,2,5,8,3,6), (1,5)(2,6)(3,7)(4,8), (1,6,3,8,5,2,7,4), (1,7,5,3)(2,8,6,4), (1,8,7,6,5,4,3,2)

n=9
(1), (1,2,3,4,5,6,7,8,9), (1,3,5,7,9,2,4,6,8), (1,4,7)(2,5,8)(3,6,9), (1,5,9,4,8,3,7,2,6), (1,6,2,7,3,8,4,9,5), (1,7,4)(2,8,5)(3,9,6), (1,8,6,4,2,9,7,5,3), (1,9,8,7,6,5,4,3,2)

n=10
(1), (1,2,3,4,5,6,7,8,9,10), (1,3,5,7,9)(2,4,6,8,10), (1,4,7,10,3,6,9,2,5,8), (1,5,9,3,7)(2,6,10,4,8), (1,6)(2,7)(3,8)(4,9)(5,10), (1,7,3,9,5)(2,8,4,10,6), (1,8,5,2,9,6,3,10,7,4), (1,9,7,5,3)(2,10,8,6,4), (1,10,9,8,7,6,5,4,3,2)

n=11
(1), (1,2,3,4,5,6,7,8,9,10,11), (1,3,5,7,9,11,2,4,6,8,10), (1,4,7,10,2,5,8,11,3,6,9), (1,5,9,2,6,10,3,7,11,4,8), (1,6,11,5,10,4,9,3,8,2,7), (1,7,2,8,3,9,4,10,5,11,6), (1,8,4,11,7,3,10,6,2,9,5), (1,9,6,3,11,8,5,2,10,7,4), (1,10,8,6,4,2,11,9,7,5,3), (1,11,10,9,8,7,6,5,4,3,2)

n=12
(1), (1,2,3,4,5,6,7,8,9,10,11,12), (1,3,5,7,9,11)(2,4,6,8,10,12), (1,4,7,10)(2,5,8,11)(3,6,9,12), (1,5,9)(2,6,10)(3,7,11)(4,8,12),(1,6,11,4,9,2,7,12,5,10,3,8), (1,7)(2,8)(3,9)(4,10)(5,11)(6,12), (1,8,3,10,5,12,7,2,9,4,11,6), (1,9,5)(2,10,6)(3,11,7)(4,12,8), (1,10,7,4)(2,11,8,5)(3,12,9,6), (1,11,9,7,5,3)(2,12,10,8,6,4), (1,12,11,10,9,8,7,6,5,4,3,2)