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Sylow P Subgroup
Definition: Let G be a group of order n, and let p be a prime integer that divides n. Let p^e denote the largest power of p that divides n, so that n=(p^e)m, where m is an integer not divisible by p. Subgroups H of G of order p^e are called Sylow p-subgroups of G. A Sylow p-subgroup is a p-group whose index in the group isn't divisible by p.
Source: Algebra, second edition by Michael Artin