GroupTheory
SpecialUnitaryGroup
construct a permutation group isomorphic to a special unitary group
Calling Sequence
Parameters
Description
Examples
Compatibility
SpecialUnitaryGroup(n, q)
n
-
a positive integer
q
power of a prime number
The special unitary group SU⁡n,q is the set of all n x n matrices over the field with q2 elements whose determinant is 1 and respect a fixed nondegenerate sesquilinear form.
The SpecialUnitaryGroup( n, q ) command returns a permutation group isomorphic to the special unitary group SU⁡n,q .
Note that for n=2 the groups SU⁡n,q and SL⁡n,q are isomorphic so the latter is returned in this case.
The ranges for n and q are as follows:
n=2
q≤100
n=3
q≤10
n=4
q≤4
n=5
q≤3
n=6,7
q=2
If either or both of the parameters n and q is non-numeric, then a symbolic group representing the indicated special unitary group is returned.
In the Standard Worksheet interface, you can insert this group into a document or worksheet by using the Group Constructors palette.
with⁡GroupTheory:
G≔SpecialUnitaryGroup⁡3,2
G≔SU3,2
Generators⁡G
2,3,5,94,7,13,226,11,19,268,15,17,2010,18,25,2412,21,27,23,1,2,4,8,16,24,21,7,14,11,20,273,6,12,5,10,9,17,18,19,25,22,2613,23,15
IsTransitive⁡G
true
GroupOrder⁡SpecialUnitaryGroup⁡4,2
25920
G≔SpecialUnitaryGroup⁡2,23
G≔SL2,23
ClassNumber⁡G
27
GroupOrder⁡SpecialUnitaryGroup⁡3,q
q3⁢q2−1⁢q3+1
MinPermRepDegree⁡SpecialUnitaryGroup⁡3,5
378
The GroupTheory[SpecialUnitaryGroup] command was introduced in Maple 17.
For more information on Maple 17 changes, see Updates in Maple 17.
The GroupTheory[SpecialUnitaryGroup] command was updated in Maple 2020.
See Also
GroupTheory[ClassNumber]
GroupTheory[Generators]
GroupTheory[GroupOrder]
GroupTheory[IsTransitive]
GroupTheory[ProjectiveSpecialUnitaryGroup]
GroupTheory[SpecialLinearGroup]
Download Help Document
What kind of issue would you like to report? (Optional)