objects generated with an isomorph-rejection technique such as this provides a way of checking that Burnside's Lemma was correctly applied. History: the lemma that is not Burnside's William Burnside stated and proved this lemma, attributing it to , in his 1897 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 (see also Stigler's law of eponymy). This is less ambiguous than it may seem: Burnside contributed many lemmas to this field. See also Pólya enumeration theorem Cycle index Notes References Also available here at Archive.org. (This is the first edition; the introduction to the second edition contains Burnside's famous volte face regarding the utility of representation theory.) . . . . Lemmas in group theory