Dear Martin, coming back to an initial question asked by Alexander, your examples seem to indicate that *isomorphism as abstract groups* is not the appropriate notion of equivalence.
When groups arise as symmetries of finite sets such as the vertices of graphs then it is more natural to consider *permutation isomorphism* (that is, conjugacy in the symmetric group on the given points). For example, a group of order two can act on four points by swapping two pairs or by fixing two points and swapping the other two points; these two possibilities should probably be distinguished in such a context. With respect to permutation isomorphism, groups are considered as small when they are permutation groups on a small set, regardless of their group orders. GAP's library of transitive groups provides a reasonable source of small groups in this sense. All the best, Thomas On Sun, Dec 17, 2017 at 08:58:45AM +0100, Martin Rubey wrote: > Dear Alexander Hulpke, Dear Forum, > > many many thanks for your comments! Let me try to clarify - I apologize > for the lengthy text... > > > There is no fundamental obstacle, but you either will end up with just > > referring to some of the libraries of groups, or end up with an > > exceeding amount of work by hand to make things come out nicely: > > > > - What groups are you planning to classify? Abstract groups or > > Permutation groups (i.e. group actions)? > > the idea is to have finite abstract groups in findstat. > [...] _______________________________________________ Forum mailing list Forum@gap-system.org https://mail.gap-system.org/mailman/listinfo/forum
