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Automorphisms of the symmetric and alternating groups
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Automorphisms of the symmetric and alternating groups : ウィキペディア英語版
Automorphisms of the symmetric and alternating groups
In group theory, a branch of mathematics, the automorphisms and outer automorphisms of the symmetric groups and alternating groups are both standard examples of these automorphisms, and objects of study in their own right, particularly the exceptional outer automorphism of ''S''6, the symmetric group on 6 elements.
== Summary ==
(S_n)
|-----
| n\neq 2,6
| S_n
| 1
|-----
| n=2
| 1
| 1
|-----
| n=6
| S_6 \rtimes C_2
| C_2
|}
(A_n)
|-----
| n\geq 4, n\neq 6
| S_n
| C_2
|-----
| n=1,2
| 1
| 1
|-----
| n=3
| C_2
| C_2
|-----
| n=6
| S_6 \rtimes C_2
| V=C_2 \times C_2
|}

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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