Burnside's lemma
lemma stating that, given a finite group G acting on a set, the number of orbits times |G| equals the sum (over every element of G) of the numbers of fixed points
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Burnside's lemma
Summary
Burnside's lemma is a theorem[1]. It ranks in the top 8% of theorem entities by monthly Wikipedia readership (323 views/month).[2]
Key Facts
- Burnside's lemma is credited with the discovery of Augustin-Louis Cauchy[3].
- Burnside's lemma is credited with the discovery of Ferdinand Georg Frobenius[4].
- Burnside's lemma's instance of is recorded as theorem[5].
- William Burnside is named after Burnside's lemma[6].
- Augustin-Louis Cauchy is named after Burnside's lemma[7].
- Ferdinand Georg Frobenius is named after Burnside's lemma[8].
- Burnside's lemma's Freebase ID is recorded as /m/01lcxr[9].
- Burnside's lemma's defining formula is recorded as |X/G|=\frac1{|G|}\sum_{g\in G}|X^g|[10].
- Burnside's lemma's MathWorld ID is recorded as Cauchy-FrobeniusLemma[11].
- Burnside's lemma's maintained by WikiProject is recorded as WikiProject Mathematics[12].
- Burnside's lemma's copyright status is recorded as public domain[13].
- Burnside's lemma's Microsoft Academic ID is recorded as 67922486[14].
- Burnside's lemma's Brilliant Wiki ID is recorded as burnsides-lemma[15].
- Burnside's lemma's ProofWiki ID is recorded as Burnside's_Lemma[16].
- Burnside's lemma's in defining formula is recorded as G[17].
- Burnside's lemma's in defining formula is recorded as X[18].
- Burnside's lemma's in defining formula is recorded as |G|[19].
- Burnside's lemma's in defining formula is recorded as X^g[20].
- Burnside's lemma's in defining formula is recorded as X/G[21].
- Burnside's lemma's Encyclopedia of Mathematics article ID is recorded as Burnside_Lemma[22].
- Burnside's lemma's Group Properties article ID is recorded as Orbit-counting_theorem[23].
Body
Works and Contributions
Credited discoveries include Augustin-Louis Cauchy[3], a mathematician[24], 1789–1857[25], of France[26], awarded the Pour le Mérite for Sciences and Arts order[27], specialised in mathematical analysis[28] and Ferdinand Georg Frobenius[4], a mathematician[29], 1849–1917[30], of Kingdom of Prussia[31], specialised in algebra[32].
Why It Matters
Burnside's lemma ranks in the top 8% of theorem entities by monthly Wikipedia readership (323 views/month).[2] It has Wikipedia articles in 16 language editions, a strong signal of global cultural recognition.[33] It is known by 17 alternative names across languages and contexts.[34]