Two Results for Automorphism Group of Partially Commutative Class Two Nilpotent Groups

Let $\Gamma$ be a finite simle graph, $R$ be a binomial ring and $G_{\Gamma}$, be a partially commutative $R$-group of nilpotency class $2$ coresponded to graph $\Gamma$. In recent paper [1] "Structure of the automorphism group for partially commutative class two nilpotent groups" author jointly with V.N. Remeslennikov reduced the study of $Aut(G_{\Gamma})$ to the study of its unipotent part $UT(G_{\Gamma})$. In this paper we compute the nilpotency class for $UT(G_{\Gamma})$ and give generating set for $UT(G_{\Gamma})$. Moreover, we descibe generating set for $Aut(G_{\Gamma})$.