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Owner confidence rating: High Entry average rating: No information on entry rating
Sylow theorems (Theorem)

Let $ G$ be a finite group whose order is divisible by the prime $ p$. Suppose $ p^m$ is the highest power of $ p$ which is a factor of $ \vert G\vert$ and set

$\displaystyle k = \frac{\vert G\vert}{p^m}.$
Then
  1. the group $ G$ contains at least one subgroup of order $ p^m$,
  2. any two subgroups of $ G$ of order $ p^m$ are conjugate, and
  3. the number of subgroups of $ G$ of order $ p^m$ is congruent to $ 1$ modulo $ p$ and is a factor of $ k$.



"Sylow theorems" is owned by yark. [ full author list (3) | owner history (5) ]
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See Also: Sylow p-subgroup, groups of order pq, Sylow's first theorem, Sylow's third theorem, Hall subgroup


Attachments:
proof of Sylow theorems (Proof) by Henry
groups of order pq (Example) by yark
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Cross-references: congruent, number, conjugate, subgroup, contains, group, factor, power, prime, divisible, order, finite group
There are 10 references to this entry.

This is version 3 of Sylow theorems, born on 2002-02-19, modified 2008-03-06.
Object id is 2243, canonical name is SylowTheorems.
Accessed 7426 times total.

Classification:
AMS MSC: 20D20 (Group theory and generalizations :: Abstract finite groups :: Sylow subgroups, Sylow properties, $\pi$-groups, $\pi$-structure)
Pending Errata and Addenda
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