Generating infinite symmetric groups
| dc.creator | Bergman, George M. | |
| dc.date | 2004-01-22 | |
| dc.date | 2005-05-27 | |
| dc.date.accessioned | 2026-07-07T08:06:13Z | |
| dc.date.available | 2026-07-07T08:06:13Z | |
| dc.description | Let S=Sym(Ω) be the group of all permutations of an infinite set Ω. Extending an argument of Macpherson and Neumann, it is shown that if U is a generating set for S as a group, respectively as a monoid, then there exists a positive integer n such that every element of S may be written as a group word, respectively a monoid word, of length \leq n in the elements of U. Several related questions are noted, and a brief proof is given of a result of Ore's on commutators that is used in the proof of the above result. | |
| dc.description | 9 pages. See also http://math.berkeley.edu/~gbergman/papers To appear, J.London Math. Soc.. Main results as in original version. Starting on p.4 there are references to new results of others including an answer to original Question 8; "sketch of proof" of Lemma 11 is replaced by a full proof; 6 new references | |
| dc.identifier | https://arxiv.org/abs/math/0401304 | |
| dc.identifier | http://arxiv.org/abs/math/0401304 | |
| dc.identifier | Bull. London Math. Soc. 38 (2006) 429-440 | |
| dc.identifier | doi:10.1112/S0024609305018308 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/130529 | |
| dc.subject | Group Theory | |
| dc.subject | 20B30 (primary), 20B07, 20E15 (secondary) | |
| dc.title | Generating infinite symmetric groups | |
| dc.type | text |