This article is about a GAP function.
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.
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.
For the function as a whole
The memory usage for the function is 1540.
For particular groups constructed using the functionPLACEHOLDER FOR INFORMATION TO BE FILLED IN: [SHOW MORE]
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