Dear GAP Forum, I've been writing code that given a finite group G, computes actions on the set of conjugacy classes of generating pairs of G. To implement this action I've been working with "minimum representatives" of each conjugacy class - ie, given a generating pair (g,h) of G, I instead will work with the pair (g',h'), defined as follows:
g' := Minimum(List(ConjugacyClass(G,g))); t := RepresentativeAction(G,g,g'); C := Centralizer(G,g); h' := Minimum(List(Orbit(C,h^t))); Thus, (g',h') is the "minimum" element of the conjugacy class of (g,h), under the lexicographic ordering built on the internal ordering on G which is used by the function "Minimum". I've built a bunch of sanity checks into my code, and so far there hasn't been any issues, but I wonder - is it possible that I've just been lucky? (I've tried using "safer" implementations of the action, but they generally run slower than just operating on minimum objects as defined above - unless anyone has any ideas?) In other words, given a finite group G represented in GAP, is G guaranteed to have an immutable total ordering which "Minimum" is always guaranteed to use when called via "Minimum(List(X))" where X is a subset of G? - Will -- William Chen Member, School of Mathematics Institute for Advanced Study, Princeton, NJ, 08540 oxei...@gmail.com _______________________________________________ Forum mailing list Forum@mail.gap-system.org http://mail.gap-system.org/mailman/listinfo/forum
