GroupElementToWord

GroupElementToWord[group,g]

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

Details 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 {m1,,mk} 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.

Examples

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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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Out[2]=

Reconstruct the permutation from the word:

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Out[3]=

Scope  (2)

Options  (3)

Applications  (1)

Properties & Relations  (4)

Neat Examples  (1)

See Also

GroupElementFromWord  GroupGenerators  GroupElements  PermutationGroup

Tutorials

Introduced in 2012
(9.0)