return the degree of a permutation group
return the set of points moved by a permutation group
return the number of points moved by a permutation group
return the smallest point moved by a permutation group
return the largest point moved by a permutation group
Degree( G )
Support( G )
SupportLength( G )
MinSupport( G )
MaxSupport( G )
a permutation group
The degree of a permutation group is the cardinality of the set upon which it acts. Since permutation groups act on sets of the form 1,2,…,n, the degree is the positive integer n. In other words, the degree n is the smallest positive integer such that G is a subgroup of Sn .
The Degree( G ) command returns the degree of a permutation group G.
Some group constructors, such as those for the symmetric and alternating groups take a degree parameter as input, and the Degree command returns this value.
The support of the permutation group G is the set of positive integers displaced by some member of G.
The Support( G ) command returns the support of G as a Maple set of positive integers.
The SupportLength( G ) command returns the cardinality of the support of G. Note that this may differ from the degree of G.
The MinSupport( G ) command returns the smallest positive integer that is displaced by the permutation group G. Similarly, the MaxSupport( G ) command returns the largest positive integer displaced by some member of G.
G ≔ Group⁡Perm⁡1,2,Perm⁡2,3,4
G ≔ DihedralGroup⁡14
G ≔ AlternatingGroup⁡10
G ≔ Group⁡Perm⁡2,4,7,Perm⁡4,7
The GroupTheory[Degree], GroupTheory[Support], GroupTheory[SupportLength], GroupTheory[MinSupport] and GroupTheory[MaxSupport] commands were introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
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