On Wednesday, September 10, 2014 11:51:55 AM UTC-7, Martin R wrote:
>
> I think that's what PermutationGroup and PermutationGroupElement do.

No:

sage: PermutationGroupElement((2,3,4)).parent()
Symmetric group of order 4! as a permutation group
sage: PermutationGroupElement([1,2,3]).parent()
Symmetric group of order 3! as a permutation group

They live in Sym({1,...,n}) (where n is somehow divined from the input), 
not in the injective limit of those things.

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