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Sylow theorems

A collection of theorems concerning the number and properties of subgroups of prime power order in a finite group.
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The statement of the theorem

For a prime pp dividing ∣G∣|G|, Sylow pp-subgroups exist, form a single conjugacy class, and their number npn_p satisfies np≡1(modp)n_p \equiv 1 \pmod p and np∣∣G∣n_p \mid |G|.
Source: Wikipedia