Let be a Prime Number, a Group, and the order of .

- 1. If divides , then has a Sylow
*p*-Subgroup. - 2. In a Finite Group, all the Sylow
*p*-Subgroup are isomorphic for some fixed . - 3. The number of Sylow
*p*-Subgroup for a fixed is Congruent to 1 (mod ).

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1999-05-26