Word problem in finite permutation groups as monoids

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Christian Stump

May 4, 2016, 8:28:28 AM5/4/16
to sage-support
The method "word_problem" for a permutation group element can be found at


But if the permutation group G is finite, I wonder whether I can also obtain a shortest word of an element w in G that does not use the inverses? This is, is there a way to get a word in M(G) = < g1, ... gm >_{monoid} as a monoid (of course M(G) = G as sets for G finite)?

If this is not yet anywhere in Sage, is there maybe a function in gap that does provide that, which I could wrap?

One simple example would be:

    sage: pi
    sage: G.gens()

    sage: pi.word_problem(G.gens(),False)[0]

    sage: pi.not_existing_word_problem_method_as_monoid(G.gens())

Thanks! Christian
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