GroupElementFromWord

GroupElementFromWord[group, w]
returns the element of group determined by the word w in the generators of group.

DetailsDetails

  • In GroupElementFromWord[group, w], the word w must be 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)

For a given list of group generators, this word represents the product of the first generator with itself and then with inverse of the second generator:

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For the dihedral group of order 16, the word corresponds to the element:

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The same result can be obtained by multiplying the generators explicitly:

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