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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Remeslennikov V. N., Treier A. V., “Struktura gruppy avtomorfizmov dlya chastichno kommutativnykh dvustupenno nilpotentnykh grupp”, Algebra i logika, 49:1 (2010), 60–97 | MR | Zbl

[2] Mischenko A. A., Treier A. V., “Grafy kommutativnosti dlya chastichno kommutativnykh dvustupenno nilpotentnykh $Q$-grupp”, Sibirskie elektronnye matematicheskie izvestiya, 2007, no. 4, 460–481 | MR

[3] Sib. Math. J., 5:23 (1982), 711–724 | MR | Zbl

[4] Hall P., “Nilpotent Groups”, Canad. Math. Congr. Summer. Sem., Univ. of Alberta, Edmonton, 1957 ; reprint, The Edmonton Notes on Nilpotent Groups, Queen Mary College, L., 1969 | Zbl | Zbl