# GAP:GeneralLinearGroup

From Groupprops

This article is about a 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 `GeneralLinearGroup` and `GL`.

### Behavior

- If the first argument is a positive integer and the second argument is a prime power , the argument returns the general linear group of degree (i.e., of matrices) over the field of elements.
- If the first argument is a positive integer and the second argument is a ring, the argument returns the general linear group of degree 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 NoMethodFound error.

## Related functions

## Examples of usage

Here is an example:

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

Here is another example:

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) ])