Theorem 1 (Burnside’s Theorem).
From this we immediately get
A group of order , where are prime, cannot be a nonabelian simple group.
Now, each divides , but cannot be since the center is trivial. It cannot be a power of either or by Burnside’s theorem. Thus for each and thus , which is a contradiction. ∎
Finally, a corollary of the above is known as the Burnside - Theorem (http://planetmath.org/BurnsidePQTheorem).
A group of order is solvable.
|Date of creation||2013-03-22 16:38:14|
|Last modified on||2013-03-22 16:38:14|
|Last modified by||rm50 (10146)|