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2009-08-19T23:19:35Z

Created page with '{{GAP function}} ==Definition== ===Function type=== This function takes as input two arguments, the first of which is a positive integer, and the second is either a ring or a …'

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{{GAP function}}

==Definition==

===Function type===

This function takes as input two arguments, the first of which is a positive integer, and the second is either a ring or a prime power.

The function can be called using either <tt>GeneralLinearGroup</tt> and <tt>GL</tt>.

===Behavior===

* If the first argument is a positive integer <math>n</math> and the second argument is a prime power <math>q</math>, the argument returns the [[general linear group]] of degree <math>n</math> (i.e., of <math>n \times n</math> matrices) over the field of <math>q</math> elements.
* If the first argument is a positive integer <math>n</math> and the second argument is a ring, the argument returns the [[general linear group]] of degree <math>n</math> over that ring.
* If the second argument is an integer that is not a prime power, GAP returns a usage error.
* If the first argument is an integer that is not positive, GAP returns a [[GAP:NoMethodFound|NoMethodFound]] error.

==Related functions==

* [[GAP:SpecialLinearGroup]]

==Examples of usage==

Here is an example:

<pre>gap> G := GL(2,3);
GL(2,3)
gap> IdGroup(G);
[ 48, 29 ]
gap> IsSolvable(G);
true</pre>

Here is another example:

<pre>gap> G := GeneralLinearGroup(3,5);
GL(3,5)
gap> C := Center(G);
<group of 3x3 matrices in characteristic 5>
gap> H := G/C;
Group([ (8,11,10,9)(12,27,22,17)(13,31,25,19)(14,28,26,20)(15,29,23,21)(16,30,24,18), (1,2,7,10,25,3,12,9,20,31,18,21,16,24,4,17,11,30,13,29,28,23,5,
22)(6,27,8,15,19,26) ])</pre>

GAP:GeneralLinearGroup - Revision history

Vipul: Created page with '{{GAP function}} ==Definition== ===Function type=== This function takes as input two arguments, the first of which is a positive integer, and the second is either a ring or a …'