General linear group over integers

Definition
Let $$n$$ be a natural number. The general linear group of order $$n$$ over integers, denoted $$GL(n,\mathbb{Z})$$ or $$GL_n(\mathbb{Z})$$, is defined in the following equivalent ways:


 * 1) It is the general linear group of order $$n$$ over the ring $$\mathbb{Z}$$, defined as the ring of integers.
 * 2) It is the automorphism group of the free abelian group of rank $$n$$, i.e., the group $$\mathbb{Z}^n$$.