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Burnside lemma

For a finite group

G

acting on a finite set

X

, the number of orbits is

∣ X / G ∣ = \frac{1}{∣ G ∣} \sum_{g \in G} ∣ X^{g} ∣.

It follows by counting pairs

(g, x)

with

gx = x

first by

g

and then by

x

.

Table of contents 72 1
- Permutation representation of a two-transitive action Burnside lemma 37

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