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Tim Hsu writes in his e-mail article of 1994/04/13

Hi. I would like to be able to do the following thing: I have a

presentation of a finite group G, and I would like to be able to know,

say, the 100 "shortest" ways of expressing a word in the generators

which represents the identity in G as a product of conjugates of

relators. Is this easy to do in GAP? If not, do you know of another

program which does this?

This is similar to the word problem, so I very much doubt that a good

deterministic algorithm exists. What you could do is to systematically

enumerate the words in the relators and just check whether or not such a

word simplifies in the free group to the given word. Obviously this

will only work if the given word has a rather short representation as

word in the relators.

Another possibility might be to add the given word to the generators, and

then to use Tietze transformations to get rid of the word again. If one

keeps track of the transformations, this could be used to write the given

word in the original relators. This is, however, not very likely to

give the shortest such representation.

Martin.

-- .- .-. - .. -. .-.. --- ...- . ... .- -. -. .. -.- .- Martin Sch"onert, Martin.Schoenert@Math.RWTH-Aachen.DE, +49 241 804551 Lehrstuhl D f"ur Mathematik, Templergraben 64, RWTH, 52056 Aachen, Germany

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