Generating infinite symmetric groups
Abstract
Let S=Sym(\Omega) be the group of all permutations of an infinite set \Omega. 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 January 2004
 arXiv:
 arXiv:math/0401304
 Bibcode:
 2004math......1304B
 Keywords:

 Mathematics  Group Theory;
 20B30 (primary);
 20B07;
 20E15 (secondary)
 EPrint:
 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