Generating Countable Sets of Permutations |
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Authors: | Galvin Fred |
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Institution: | Department of Mathematics, University of Kansas Lawrence, Kansas 66045-2142, USA |
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Abstract: | 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 answerto a question of Macpherson and Neumann, I show that, if Sym(E)is generated by A B where |B| ||E||, then Sym(E) is generatedby A { } for some permutation in Sym(E). |
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