I want to show, that $GL\_n(\mathbb{Z}/b\mathbb{Z})$ operates transitively on 
$X = \{ (v\_1, \ldots, v\_n) \in (\mathbb{Z}/b\mathbb{Z})^n \ | \ v\_1\mathbb{Z}/b\mathbb{Z} + \ldots + v\_n\mathbb{Z}/b\mathbb{Z} = \mathbb{Z}/b\mathbb{Z}\} $  

($b$ is an integer.)


IOW


1. $A \in GL\_n(\mathbb{Z}/b\mathbb{Z}), x \in X \Rightarrow Ax \in X$
2. For all $x,y \in X$ exists $A \in GL\_n(\mathbb{Z}/b\mathbb{Z})$ such that $x = Ay$.


I have no idea, where to start.


Thanks  

-elfinit



Operation of GL_n(Z/bZ)
Any transformation
$$(v\_1,\ldots,v\_n)\mapsto (v\_1,\ldots,v\_{j-1},v\_j+av\_k,v\_{j+1},\ldots,v\_n)$$
for $j\ne k$ is achievable by means of some such matrix. It suffices to reduce
an admissible vector to $(1,0,\ldots,0)$ by means of a sequence of such reductions.
I would do it in three stages


1. Make $v\_n$ into a unit in $\mathbb{Z}/b\mathbb{Z}$;
2. Make $v\_1=1$;
3. Make all $v\_j=0$ for $j>1$.


