[GAP Forum] Canonical form for some small groups and efficient characterisation of the generalized symmetric groups

[Christopher Jefferson]

> On Dec 19, 2017, at 7:44 PM, Rubey Martin <martin.rubey at tuwien.ac.at> wrote:
> 
>> In the same way that nasty can calculate both graph automorphism and graph canonical image, I am working on extending Partition Backtrack to solve both the conjugacy problem and the canonical image problem for groups, expect a release next year.
> 
> This sounds like wonderful news!
> 
>> However, having a “sensible string” is probably impossible. Nauty doesn’t produce a “sensible string” to describe the automorphism of graphs.
> 
> I should have been clearer: a short list of generators for the representative of the conjugacy class would be just fine.  I am guessing that that's not impossible, right?

Producing some small list is easy, GAP does it all the time.

I don’t know about producing a small repeatable list (that is, a function which always produce the same list regardless of the generators you start with). I suspect coming up with something involving stabilizer chains is possible.

Chris