Talk:Free group

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Mathematics rating: Start Class High Priority  Field: Algebra

Question, is the reason that a free abelian group is not the same as an abelian free group is that in an free group ab ≠ ba, necessarily, but in an abelian free group, a+b=b+a?

-- Very nice page. After spending an hour staring at Hungerford's definition, it's nice to see the clear underlying idea. Thanks. 134.243.218.123 23:11, 22 March 2006 (UTC)

[edit] Possible revision and expansion

Hi everyone!

I've been working on a possible revision and expansion of this article for a while. Parts of it are now in good enough shape that it might make sense to move them into the main article in some form. Let me know what you think:

Please be aware that when I'm writing a draft, I tend to rewrite as much text as possible, on the theory that we can use whichever version comes out better. Jim 20:24, 22 September 2007 (UTC)

I don't think that what you have prepared is any way acceptable as a substitute for the present page. It is amateur and short on any extra useful information. This is not the way WP articles are written. Mathsci 21:22, 22 September 2007 (UTC)
I'm really not proposing replacing this page with the draft. I wrote a bunch of stuff, and now I'm proposing moving the best of it to this page. Please take a look and see if you like any of it. :-) Jim 21:29, 22 September 2007 (UTC)
It's probably best to follow normal pratice and add little bits at a time. Don't remove anything: there's a lot that you haven't included in your version and some of it is not concise or encyclopedic. The references of Magnus et al and Serre are classics. There is incidentally the whole connection of the lower central series of the free group and free Lie algebras due to Magnus that has not yet been covered; also Haagerup-Gromov a-T-menability of the free group. So please just add extra details bit by bit, trying to be as concise and general as possible, and don't attempt to rewrite the whole article. Mathsci 21:45, 22 September 2007 (UTC)

All right, I'll just go ahead and post some things. Feel free to undo any revisions you dislike. Jim 22:29, 22 September 2007 (UTC)

Looks good. I just reinstated the fact about the naming of free groups and made a reference to Magnus' work on free Lie algebras. Your way of including references in the text makes it a little bit hard to edit the original. Please try to avoid this if you change any of the mathematics sections: just add references at the end. Mathsci 11:58, 23 September 2007 (UTC)
You have now started adding trivialities. The rank of a free group is the rank of its abelianisation as a free Abelian group. What you added is long-winded and mathematically obvious. It's exactly what is not wanted in this article. Why not read the chapter on commutators in Magnus' book? (This is the first case G/G'.) The problem with what you have added is exactly what was wrong with your draft article. Sorry. Mathsci 18:35, 23 September 2007 (UTC)
I'm sorry that you didn't like that section, but I think its contents would be non-obvious to someone who wasn't a group theorist. In any case, I'm happy to work on other articles instead. Jim 19:14, 23 September 2007 (UTC)
This is a little bit WP:POV, don't you think? If you look at the history of the page, you might get some idea of consensus and of the level of the article. But what's wrong with Ab(G)=G/G'? When I came across this article, I was surprised to find no mention of group actions on trees. Mathsci 19:51, 23 September 2007 (UTC)

the contents of the topology and geometry sections from Jim's draft, in more concise form perhaps, can help provide additional examples/perspectives. Mct mht 05:53, 29 September 2007 (UTC)