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GroupTheory

 GeneralLinearGroup
 construct a permutation group isomorphic to the General Linear Group over a finite field

 Calling Sequence GeneralLinearGroup(n, q) GL( n, q )

Parameters

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

Description

 • The general linear group $GL\left(n,q\right)$ is the set of all nonsingular $n×n$ matrices over a finite field of size $q$, where $q$ is a prime power.
 • The GeneralLinearGroup( n, q ) command returns a permutation group isomorphic to the general linear group $GL\left(n,q\right)$ for the implemented ranges of the parameters n and q.
 • The implemented ranges for n and q are as follows:

 $n=2$ $q\le 100$ $n=3$ $q\le 20$ $n=4$ $q\le 10$ $n=5$ $q\le 5$ $n=6,7,8,9,10$ $q=2$

 • The abbreviation GL( n, q ) is available as a synonym for GeneralLinearGroup( n, q ).

Examples

 > $\mathrm{with}\left(\mathrm{GroupTheory}\right):$
 > $\mathrm{GeneralLinearGroup}\left(2,3\right)$
 ${\mathbf{GL}}\left({2}{,}{3}\right)$ (1)
 > $\mathrm{GL}\left(4,3\right)$
 ${\mathbf{GL}}\left({4}{,}{3}\right)$ (2)
 > $\mathrm{GroupOrder}\left(\mathrm{GL}\left(3,q\right)\right)$
 $\left({{q}}^{{3}}{-}{1}\right){}\left({{q}}^{{3}}{-}{q}\right){}\left({{q}}^{{3}}{-}{{q}}^{{2}}\right)$ (3)

Compatibility

 • The GroupTheory[GeneralLinearGroup] command was introduced in Maple 17.
 • For more information on Maple 17 changes, see Updates in Maple 17.