Remark

Tag 05E3, permanent. Cite it as [Bourbaki, Tag 05E3].

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

For every prime number q dividing Card(G), let P_q be a Sylow q-subgroup of G. Then the subgroup H of G generated by the P_q is of order a multiple of Card(P_q) for each q and of order a divisor of Card(G), hence it is equal to G.

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

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Cites

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