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Sylow Theorems


Let p be a prime number, G a finite group, and |G| the order of G.

1. If p divides |G|, then G has a Sylow p-subgroup.

2. In a finite group, all the Sylow p-subgroups are conjugate for some fixed p.

3. The number of Sylow p-subgroups for a fixed p is congruent to 1 (mod p).


See also

Conjugate Subgroup, Sylow p-Subgroups

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Cite this as:

Weisstein, Eric W. "Sylow Theorems." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SylowTheorems.html

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