Talk:Thompson groups
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conjecture[edit]
Trying to trace the source of the statement about the Von Neumann conjecture.
Charles Matthews 06:33, 18 May 2004 (UTC)
Err - which statement? If you mean the statement that the conjecture has been disproved then I presume you've now found one as you've added details to the Von Neumann conjecture page. The statement that F, if proven not to be amenable, would be another counterexample, follows immediately from the fact that it doesn't contain a rank 2 free subgroup. The latter is well-known, but I can probably hunt out a reference if you think it needs one..... Best wishes, Cambyses 16:51, 18 May 2004 (UTC)
Yes, I later found a web reference to a f.p. counterexample. But maybe (I'm less clear) this wasn't the first counterexample to the vN conjecture . It seems there may have been some counterexample a fair few years ago.
Charles Matthews 17:19, 18 May 2004 (UTC)
We don't know[edit]
Please note that J. Moore no longer claims that F is amenable: http://arxiv.org/abs/1209.2063 "Over the weekend of September 29-30, 2012, Azer Akhmedov pointed out a serious error in Lemma 4.13. This error appears to be both serious and irreparable. I therefore withdraw my claim of a proof that F is amenable". T.K. — Preceding unsigned comment added by 2.100.216.103 (talk) 20:02, 2 January 2013 (UTC)