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Mathematica > Mathematics and Algorithms > Discrete Mathematics > Group Theory > Named Groups > AlternatingGroup >

BUILT-IN MATHEMATICA SYMBOL

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: