GAP:SpecialLinearGroup

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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 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

Memory usage

For the function as a whole

The memory usage for the function is 1540.

For particular groups constructed using the function

PLACEHOLDER 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