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Third Sylow Theorem

  • Definition: Let G be a finite group whose order n is divisible by a prime p. Say that n=(p^e)m, where p does not divide m, and let s denote the number of Sylow p-subgroups. Then s divides m and s is congruent to 1 modulo p; s=kp+1 for some integer k >= 0.

    Source: Algebra, second edition by Michael Artin

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