- #1
mathplease
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If G is a permutation group acting on a finite set A and x [tex]\in[/tex]A, then
|G| = |[tex]\Delta[/tex](x)| |Gx|
where [tex]\Delta[/tex](x) denotes the orbit containing x.
I'm having some difficulty understanding this theorem. For example,
Consider the following set G of permutations of the set M = {1,2,3,4}:
* e = (1)(2)(3)(4)
* a = (1 2)(3)(4) = (1 2)
* b = (1)(2)(3 4) = (3 4)
* ab = (1 2)(3 4)
G forms a group, so (G,M) forms a permutation group.
what is [tex]\Delta[/tex](1) in this example?
|G| = |[tex]\Delta[/tex](x)| |Gx|
where [tex]\Delta[/tex](x) denotes the orbit containing x.
I'm having some difficulty understanding this theorem. For example,
Consider the following set G of permutations of the set M = {1,2,3,4}:
* e = (1)(2)(3)(4)
* a = (1 2)(3)(4) = (1 2)
* b = (1)(2)(3 4) = (3 4)
* ab = (1 2)(3 4)
G forms a group, so (G,M) forms a permutation group.
what is [tex]\Delta[/tex](1) in this example?