Orbit-stabilizer theorem ↩

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created: 2021-12-17 18:26:14
modified: 2022-01-10 04:13:04

group acting on set

.
Statement: For every

(where

means stabilizer)

Proof

is a subgroup of and the various elements of the orbit can be identified by the left cosets of this subgroup, that is there is a one-to-one correspondence between the element () of the orbit and the coset : .

But this is easy to see: .