Dear Martin, > On 19 Dec 2017, at 16:43, Rubey Martin <martin.ru...@tuwien.ac.at> wrote: > > Dear Max, > >>>> The permutation action on the roots would be a rather natural choice. > >> Regarding Nicolas' suggestion: While it is a "natural" choice, it is not >> necessarily a "canonical" choice. At the very least, you'd have to define >> how to label the roots "canonically". > > let me ask: are you saying that that there are both "bad" but also > "canonical labellings" of the roots? (let's consider only finite type) > > Or put differently: do you have an example at hand where different labellings > of the roots yield non-conjugate permutation groups?
No, that's not what I meant. Of course any labeling with numbers 1..n can be transformed into any other by a permutation, hence the resulting permutation groups are conjugate in Sym(n). Thus any choice of such a labeling determines a conjugacy class -- but *only* that. It does not determine a representative of such a class. The question then is: How useful is that? Since you are talking about a database and finding things in it, I assumed you wanted a "canonical form" which is a string, or perhaps a tuple of integers and strings, or something "simple" like that. A conjugacy class of subgroups isn't that, though. Cheers, Max _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
