Burnside's theorem

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You might be referring to:

Result Other names What it involves
Orbit-counting theorem Burnside's lemma, Cauchy-Frobenius lemma Combinatorics, orbit counting
Burnside's basis theorem
Burnside's normal p-complement theorem
Order has only two prime factors implies solvable Burnside's p^aq^b theorem Forces groups of certain orders to be solvable.