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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 )

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As you don't specify your idea, it is not clear how to answer about "such ideas"... but perhaps the keywords you're interested in are "canonical form" or "canonical labeling"? (The latter phrase more commonly used in the context of graph isomorphism...) –  ShreevatsaR Feb 23 '13 at 19:08
but I didn't find any details about "Fingerprinting algorithms" –  J Nid Feb 23 '13 at 19:09
You don't describe your "fingerprints" and your "question" is, imo, non-understandable at all. You even say, in a rather misterious way, that you didn't find any details about "similar algorithms"...what are you talking about, anyway? –  DonAntonio Feb 23 '13 at 19:15
I have no idea about "canonical labeling" is there an equivalent concept in group theory ? –  J Nid Feb 23 '13 at 19:15
If you want our help but are not willing to even tell us what you want help about, you are not going to be much lucky! If you are worried about potential monetary value of your discovery, then it is probably a good idea not to even post about it... (You could offer valuable rewards to people who help you, but that is ideally not done in this site) –  Mariano Suárez-Alvarez Feb 23 '13 at 19:23
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closed as not a real question by DonAntonio, Jim, Norbert, Asaf Karagila, Did Feb 23 '13 at 20:31

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1 Answer

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.

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Thanks Tara 'The Handbook of Computational Group Theory' dosen't include enough details about fingerprinting –  J Nid Feb 23 '13 at 19:53
Have you tried looking in the GAP documentation and source code? –  Tara B Feb 23 '13 at 20:03
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