Geodesic
Two Results for Automorphism Group of Partially Commutative Class Two Nilpotent Groups
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 2, pp. 85-97

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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 $Aut(G_{\Gamma})$.
Keywords: partially commutative group, nilpotency, generating set, basis commutators, graph, unipotent subgroup, nilpotency step.
Mots-clés : automorphism, transvections 
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     author = {A. V. Treyer},
     title = {Two {Results} for {Automorphism} {Group} of {Partially} {Commutative} {Class} {Two} {Nilpotent} {Groups}},
     journal = {Sibirskij \v{z}urnal \v{c}istoj i prikladnoj matematiki},
     pages = {85--97},
     publisher = {mathdoc},
     volume = {10},
     number = {2},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VNGU_2010_10_2_a7/}
}
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A. V. Treyer. Two Results for Automorphism Group of Partially Commutative Class Two Nilpotent Groups. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 10 (2010) no. 2, pp. 85-97. http://geodesic.mathdoc.fr/item/VNGU_2010_10_2_a7/