GAP:SpecialLinearGroup

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

Related functions

 * GAP:GeneralLinearGroup
 * GAP:ProjectiveGeneralLinearGroup
 * GAP:ProjectiveSpecialLinearGroup

For the function as a whole
The memory usage for the function is 1540.

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