# GAP:SpecialLinearGroup

From Groupprops

(Redirected from GAP:SL)

This article is about a GAP function.

## Definition

### Function type

The function takes as input two arguments, one of which is a positive integer and the other is either a prime power or a ring.

The function can be written as `SpecialLinearGroup` or `SL`.

### Behavior

The function outputs a group stored in the matrix group format over the appropriate field of ring (the storage format can be verified using the IsMatrixGroup function).

- If the first argument is a positive integer and the second argument is a prime power , the function returns the special linear group of degree over the field of elements.
- If the first argument is a positive integer and the second argument is a ring, the function returns the special linear group of degree over the ring.

## Related functions

## Memory usage

### For the function as a whole

The memory usage for the function is 1540.

### For particular groups constructed using the function

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## Examples of usage

Here is an example that also uses GAP:GeneralLinearGroup.

gap> G := GL(2,3); GL(2,3) gap> H := SL(2,3); SL(2,3) gap> IsMatrixGroup(H); true gap> IsSubgroup(G,H); true gap> IsNormal(G,H); true

gap> G := GeneralLinearGroup(2,2); SL(2,2) gap> H := SpecialLinearGroup(2,2); SL(2,2) gap> G = H; true