Mathematica > Mathematics and Algorithms > Discrete Mathematics > Group Theory > GroupElementToWord
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GroupElementToWord

GroupElementToWord[group, g]
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:

In[1]:=
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Decompose g as a product of generators of G (negative integers represent inverse generators):

In[2]:=
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Out[2]=

Reconstruct the permutation from the word:

In[3]:=
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Out[3]=

Scope (2)Scope (2)

Options (3)Options (3)

Applications (1)Applications (1)

Properties & Relations (4)Properties & Relations (4)

Neat Examples (1)Neat Examples (1)

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