Special linear group over integers
Let be a natural number. The special linear group over integers of degree , denoted , is defined as follows:
- It is the special linear group where the base ring is set as equal to the ring of integers .
- It is a subgroup of index two in the automorphism group of the free abelian group of rank , namely, the subgroup of orientation-preserving automorphisms. The whole automorphism group is the general linear group over integers .