GroupTheory/SpecialSemilinearGroup - Maple Help
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GroupTheory

 SpecialSemilinearGroup
 construct a permutation group isomorphic to the special semi-linear group over a finite field

 Calling Sequence SpecialSemilinearGroup(n, q) SigmaL( n, q )

Parameters

 n - a positive integer q - a power of a prime number

Description

 • The special semi-linear group $\Sigma L\left(n,q\right)$ is the set of all semi-linear transformations of an $n$-dimensional vector space $V$ over the field with $q$ elements whose linear part has determinant equal to $1$.
 • If n and q are positive integers, then the SpecialSemilinearGroup( n, q ) command returns a permutation group isomorphic to the special semi-linear group  $\Sigma L\left(n,q\right)$ . Otherwise, a symbolic group is returned, for which Maple can do some limited computations.
 • The abbreviation SigmaL( n, q ) is available as a synonym for SpecialSemilinearGroup( n, q ).

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$