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Journal of the London Mathematical Society 1995 51(2):230-242; doi:10.1112/jlms/51.2.230
© 1995 by London Mathematical Society
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© The London Mathematical Society

Generating Countable Sets of Permutations

Fred Galvin

Department of Mathematics, University of Kansas Lawrence, Kansas 66045-2142, USA

Received 1 September 1993.

Let E be an infinite set. In answer to a question of Wagon, I show that every countable subset of the symmetric group Sym(E) is contained in a 2-generator subgroup of Sym(E). In answer to a question of Macpherson and Neumann, I show that, if Sym(E) is generated by A {cup} B where |B| ≤ ||E||, then Sym(E) is generated by A {cup} {{gamma}} for some permutation {gamma} in Sym(E).

This project was sponsored by the National Security Agency under Grant Number MDA904-92-H-3037.


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