  The goal of this paper is to construct and describe certain arithmetic
subgroups of the automorphism group of a partially commutative group. More
precisely, given an arbitrary finite graph $\Gamma$ we construct an arithmetic
subgroup $St(L(G))$, represented as a subgroup of $GL(n,Z)$, where $n$ is the
number of vertices of the graph $\Gamma$.
  In the last section of the paper we give a description of the decomposition
of the group of automorphisms $St^{conj}(L(G))$ as a semidirect product of the
group of conjugating automorphisms $Conj(G)$ and $St(L(G))$. This result is
closely related to Theorem 1.4 of the paper arXiv:0710.2573v1.
