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AlternatingGroup

AlternatingGroup[n]
represents the alternating group of degree n.
  • The degree n of AlternatingGroup[n] must be a non-negative integer. Degrees 0, 1, and 2 correspond to the trivial or identity group.
  • AlternatingGroup[n] is represented by default as a permutation group on the points .
Number of elements of an alternating group:
Permutation generators of an alternating group:
Elements of a permutation representation of an alternating group:
Number of elements of an alternating group:
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Permutation generators of an alternating group:
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Elements of a permutation representation of an alternating group:
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Alternating groups of degree 0, 1, or 2 are the trivial group, only containing the identity:
In all other cases the alternating group of degree n contains elements:
Test whether two random permutations generate the alternating group of degree 100:
Permute parts of an expression under the elements of an alternating group:
An alternating group contains only even permutations:
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