Definition 10

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

Algebra, chapter I, § 6. Extensions, solvable groups, nilpotent groups

Let G be a finite group. A Sylow p-subgroup of G is any subgroup P of G satisfying the two following conditions:

(a) P is a p-group. (b) (G : P) is not a multiple of p.

If the order of G is written in the form $p^r m$ , where m is not a multiple of $p$ , conditions (a) and (b) are equivalent to $\mathrm{Card}(P) = p^r$ .

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

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