MathGroup Archive 2012

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Group Elements: Changing permutation group cycles to more readable form


I'm an undergrad, in my first abstract algebra course. I'm relatively
comfortable with Mathematica, so have been using it to explore concepts
I've been learning about in the course.

Mostly I've been constructing the groups we've been learning about by
defining my own group operations on symbols, but I would like to take
advantage of the fact that the Groups we are studying are already set up in
mathematica as symmetric subgroups. The only problem is I haven't figured
out a quick and easy way to rename the cycles into the more readable and
standard element names given in my textbook, since the order in which the
elements are listed, for say, the dihedral group may or may not be the same
order mathematica gives them in. I know one can in principle figure out
which permutation corresponds to which element---I've done those exercises
in my textbook---but that's the issue, it is a bit of an exercise.

So is there any easy way to quickly assign the permutations of a named
groups to something more readable (e.g. have the elements of the dihedral
group  as a list of elements of the form r_n, s_n, as opposed to having
them as Cycle[{{1,2,3,5}].

Thank you,
Brentt Newman

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