GroupTheory
ProjectiveSpecialSemilinearGroup
construct a permutation group isomorphic to the projective special semi-linear group over a finite field
Calling Sequence
Parameters
Description
Examples
ProjectiveSpecialSemilinearGroup(n, q)
PSigmaL( n, q )
n
-
a positive integer
q
a power of a prime number
The projective special semi-linear group PΣLn,q is the quotient of the special semi-linear group ΣLn,q by the center of SLn,q .
For a positive integer n and a power q of a prime, the ProjectiveSpecialSemilinearGroup( n, q ) command returns a permutation group isomorphic to the projective special semi-linear group PΣLn,q . Otherwise, a symbolic group is returned, with which Maple can do some limited computations.
If q is a prime, then PΣLn,q and PSLn,q are the same.
The abbreviation PSigmaL( n, q ) is available as a synonym for ProjectiveSpecialSemilinearGroup( n, q ).
withGroupTheory:
G≔ProjectiveSpecialSemilinearGroup1,27
G≔PΣL1,27
GroupOrderG
3
G≔PSigmaL2,7
G≔PΣL2,7
AreIsomorphicG,PSL2,7
true
G≔PSigmaL2,9
G≔PΣL2,9
AreIsomorphicG,Symm6
G≔PSigmaL4,4
G≔PΣL4,4
IsPrimitiveG
TransitivityG
2
See Also
GroupTheory[GeneralSemilinearGroup]
GroupTheory[SpecialLinearGroup]
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