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Generating Infinite Symmetric Groups by Bergman, George M. is a scholarly article available to read on EtoBox.

What is Generating Infinite Symmetric Groups about?

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.

Author

Bergman, George M.

Published

2004

Language

EN