Proposition 21

Tag 05AA, permanent. Cite it as [Bourbaki, Tag 05AA].

In a finite group G of order n, $x^n = e$ for all $x \in G$ .

If $p$ is the order of $x$ , then $n = pq$ , with $q$ an integer, and hence $x^n = (x^p)^q = e$ .

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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