Allen Knutson's other class

Friday, November 17, 2006

Friday Nov 17

The number of p-Sylows is congruent to 1 mod p, and divides |G| / pk.
Every p-subgroup is in a Sylow.
Sylow subgroups are all conjugate.
They're normal iff they're unique.
If |G|=2p, p an odd prime, then G is either Z2p or Dp.

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