Group Elements: Changing permutation group cycles to more readable form

*To*: mathgroup at smc.vnet.net*Subject*: [mg128559] Group Elements: Changing permutation group cycles to more readable form*From*: Brentt <brenttnewman at gmail.com>*Date*: Fri, 2 Nov 2012 23:53:40 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Hello, 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