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Burnside $p$-$q$ theorem (Theorem)

Any group whose order is divisible by only two distinct primes is solvable. (These two distinct primes are the $p$ and $q$ of the title.)

It follows that if $G$ is a non-abelian finite simple group, then $\vert G\vert$ must have at least three distinct prime divisors.



"Burnside $p$-$q$ theorem" is owned by yark. [ full author list (2) | owner history (1) ]
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Cross-references: prime divisors, simple group, finite, non-Abelian, solvable, primes, divisible, order, group
There are 2 references to this entry.

This is version 5 of Burnside $p$-$q$ theorem, born on 2002-12-13, modified 2006-10-07.
Object id is 3747, canonical name is BurnsidePQTheorem.
Accessed 3281 times total.

Classification:
AMS MSC: 20D05 (Group theory and generalizations :: Abstract finite groups :: Classification of simple and nonsolvable groups)
Pending Errata and Addenda
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