A fun consequence of this is that in the group Sym(Z) of permutations of the integers, the two permutations: (0 1) and x --> 1 + x together generate a (finitely-generated!) group G which contains, as a subgroup, the group of all finitely-supported permutations (which is definitely not finitely-generated). Best wishes, Adam P. Goucher
Sent: Saturday, March 19, 2016 at 5:26 PM From: "Warren D Smith" <warren.wds@gmail.com> To: math-fun@mailman.xmission.com Subject: Re: [math-fun] generating permutations
The entire perm group S[n] is generated by the n-cycle (1,2,3,...,n) and the transposition (1,2), not sure if that suffices to make Baker happy.
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