Talk:Burnside's lemma

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Mathematics rating:	Start Class	Mid Priority	Field: Algebra
Please update this rating as the article progresses, or if the rating is inaccurate. Click to show/hide comments. Please add to or update the comments to suggest improvements to the article. References needed. Geometry guy 14:55, 21 May 2007 (UTC)

[edit] Application to Fermat's Little Theorem

If anyone has looked at the Wikipedia page called "Proofs of Fermat's Little Theorem", there is one which uses "bracelets" to establish the theorem. If you look at a proof of Cauchy's theorem given by Dr. Eyal Goren on page 79 in his course notes for an algebra course given this fall (http://www.math.mcgill.ca/goren/MATH235.2006/CourseNotesMath235.2006.pdf) you can see how the bracelet argument is virtually identical to the first part of the proof. I'm suggesting that under "example applications" we could mention that the CFF can be used to prove Fermat's Little Theorem quite easily, or even just prove it directly as a nice "sample application". feedback?

DavidKawrykow 01:23, 8 May 2007 (UTC)DavidKawrykow

The example might look better if the tabular information was formatted in a proper table. My HTML skills are weak. Is there anyone who knows what they are doing willing and able to give it a try? hawthorn

Nice Proof!

I hate this particular notation for orbits stabilsers and fixes. Unless you are very familiar with this :stuff you have to constantly look back at the definitions to see which is which and it is so easy to mix :them up. Does anyone else feel this way also? I don't suppose we could engineer a switch to the much more :instantly memorable

Orb_G(x) , Stab_G(x) and Fix_X(g)?

hawthorn

I would support that change. The proof is kind of hard to understand. FelixP 19:16, 27 May 2006 (UTC)

This article confuses two signficantly different results, the Burnside lemma (the stated identity, due to Cauchy, as Burnside knew-- he never claimed priority, and the work of Cauchy would have been known to the readers of his textbook, but some later writer apparently didn't know this literature and jumped to an incorrect conclusion), and the Polya enumeration formula (unknown to Polya, this had been previously found by Redfield). The latter explicitly refers to the cycle index of a finite group. See any good combinatorics text. For my article on Newton's identities, we need to deconflate these two results. TIA---CH (talk) 20:37, 16 August 2005 (UTC)

[edit] infinite set

Is there a good reason to allow this finite group to act on an infinite set? There are always an infinite number of orbits and the identity fixes infinitely many points, so the result is trivial then. It doesn't really hurt but maybe it reduces the understandability. McKay 07:43, 17 June 2006 (UTC)