Wolfram Language & System 10.0 (2014)|Legacy Documentation

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decomposes the group element g as a product of generators of group.

Details and OptionsDetails and Options

  • The group element g must belong to the given group.
  • GroupElementToWord[group,g] gives the word of g in the form of a list of nonzero integers representing generators in the list returned by GroupGenerators[group]. A positive integer in the word represents the ^(th) generator, and a negative integer represents the inverse of the ^(th) generator.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

Take a permutation g in a group G:

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Decompose g as a product of generators of G (negative integers represent inverse generators):

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Reconstruct the permutation from the word:

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Introduced in 2012