I have 2 algorithms to test non-isomorphic groups ( of course they do not succeed for all groups ) . Actually I am concerned that those algorithms could be considered trivial for these reasons : 1) they both require the generating of all elements of the tested groups . 2) the idea behind them is simple ( from my point of view ) but I don't know if such ideas have been used with similar algorithms ( I didn't find any details about similar algorithms ) how can i test my algorithms ? what is the best way to assess them ? where to find details about similar algorithms ( Fingerprinting algorithms )
closed as not a real question by DonAntonio, Jim, Norbert, Asaf Karagila, Did Feb 23 at 20:31
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Try searching for something like 'group isomorphism testing' rather than 'fingerprinting'. You could look at the source code for the isomorphism tests in an open-source computer algebra system like GAP. I believe GAP also has a function which identifies the isomorphism type of groups up to some order (1024 maybe?).
There is probably also some information in 'The Handbook of Computational Group Theory' by Derek Holt, Eamonn O'Brien and Bettina Eick.
In general an algorithm that requires looking at all elements of a group is very inefficient. Since you think your idea seems very simple, it's likely that it would be obvious to most computational group theorists, but they have more advanced methods that don't involve looking at all elements. However, I don't know any details about isomorphism testing algorithms though, sorry.