Elements of a permutation group in fixed order

[Rafael]

If G is a permutation group, then since G.elements is a set, I cannot
expect that list(G.elements) always lists the elements in the same
order. Can I expect that list(G.generate()) lists the elements always in
the same order?

[S.Y. Lee]

You should sort the arguments before passing to PermutationGroup.

[Aaron Meurer]

If you are using list() to get all the elements, it seems prudent to
just sort them. But it also seems like it would be useful to have an
iterator that always gives the same order, for cases where you don't
want to list all the elements.

Aaron Meurer

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[Rafael Villarroel]

Most of the time I need to work with a fixed order of the elements of the group.

I am working on representation theory, and when defining the regular representation,

the elements of the group are used as an ordered basis of a vector space, so I need

a fixed order of the elements, associated with the group.

I guess then my question is if the output of list(G.generate()) still needs to be sorted

to guarantee the fixed order, or I can do without it.

Best regards.

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