Burnside's Lemma - History: The Lemma That Is Not Burnside's

History: The Lemma That Is Not Burnside's

William Burnside stated and proved this lemma, attributing it to Frobenius 1887 in his 1887 book on finite groups. But even prior to Frobenius, the formula was known to Cauchy in 1845. In fact, the lemma was apparently so well known that Burnside simply omitted to attribute it to Cauchy. Consequently, this lemma is sometimes referred to as the lemma that is not Burnside's. This is less ambiguous than it may seem: Burnside contributed many lemmas to this field.