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math.GR2004
Closed subgroups of the infinite symmetric group
George M. Bergman, Saharon Shelah
Let S=Sym(Ω) be the group of all permutations of a countably infinite set Ω, and for subgroups G_1, G_2\leq S let us write G_1\approx G_2 if there exists a finite set U\subseteq S…
math.GR2004
Generating infinite symmetric groups
George M. Bergman
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, res…