compute the order profile of the elements of a finite group
compute the order class polynomial of a finite group
compute the order class number of a finite group
compute the order rank of a finite group
OrderClassProfile( G, opts )
OrderClassPolynomial( G, x )
OrderClassNumber( G )
OrderRank( G )
a finite group
option of the form output = "list", output = "collected" (the default), or output = "multiset"
The order class profile of a finite group G is the sequence of orders of elements of G, including their multiplicities.
The OrderClassProfile( G ) command computes the order class profile of a finite group G. By default, this is returned as a list of pairs of the form [ order, multiplicity ]. The sorted list of element orders can be returned by using the 'output' = "list" option. To produce, instead, a MultiSet, use the 'output' = "multiset" option.
The OrderClassPolynomial( G, x ) command returns a polynomial encoding of the order class data of the finite group G. It is a univariate polynomial in the indeterminate x for which the coefficient of x^k is equal to the number of elements of order k in G.
The order class number of a finite group G is the number of order classes of elements of G.
The OrderClassNumber( G ) command returns the order class number of the finite group G.
The order rank of a finite group G is the number of distinct order class lengths of G greater than 1.
The OrderRank( G ) command returns the order rank of the finite group G.
G ≔ Alt⁡4
The GroupTheory[OrderClassProfile] command was introduced in Maple 2019.
For more information on Maple 2019 changes, see Updates in Maple 2019.
The GroupTheory[OrderClassPolynomial] and GroupTheory[OrderClassNumber] commands were introduced in Maple 2020.
For more information on Maple 2020 changes, see Updates in Maple 2020.
The GroupTheory[OrderRank] command was introduced in Maple 2021.
For more information on Maple 2021 changes, see Updates in Maple 2021.
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