Generating infinite symmetric groups
نویسنده
چکیده
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 ≤ n in the elements of U. Some 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.
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