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I have a (large, finite, permutation) group, and a group element that I know is a product of length=20 of the generators. But when I ConvertGroupElementToWord, I get a word of length=118. Other, unfamiliar elements have comparably long word lengths. How do I get an optimum (shortest) word length for any element?

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  • $\begingroup$ I assume that by ConvertGroupElementToWord you mean simply the GroupElementToWord function. Nevertheless, could you clarify your question with a few more details for the non-initiated? $\endgroup$
    – MarcoB
    Commented Aug 31, 2015 at 15:09
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    $\begingroup$ Group theory is not Mathematica's strong suit. In the Options section of the docs, there are some parameters you could try to tweak, but there's not a built-in way to find the shortest word. I know it is in principle possible (en.wikipedia.org/wiki/Word_problem_for_groups) , but I'm not aware of an efficient algorithm. $\endgroup$ Commented Aug 31, 2015 at 15:23
  • $\begingroup$ See also mathoverflow.net/questions/252535/… $\endgroup$
    – user202729
    Commented Dec 8, 2018 at 15:12

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