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Vestnik Novosibirskogo Gosudarstvennogo Universiteta. Seriya Matematika, Mekhanika, Informatika, 2010, Volume 10, Issue 2, Pages 85–97
(Mi vngu43)
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Two Results for Automorphism Group of Partially Commutative Class Two Nilpotent Groups
A. V. Treyer Omsk Branch of Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences
Abstract:
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, automorphism, nilpotency, generating set, basis commutators, graph, transvections, unipotent subgroup, nilpotency step.
Received: 05.02.2010
Citation:
A. V. Treyer, “Two Results for Automorphism Group of Partially Commutative Class Two Nilpotent Groups”, Vestn. Novosib. Gos. Univ., Ser. Mat. Mekh. Inform., 10:2 (2010), 85–97
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https://www.mathnet.ru/eng/vngu43 https://www.mathnet.ru/eng/vngu/v10/i2/p85
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Abstract page: | 172 | Full-text PDF : | 82 | References: | 48 | First page: | 1 |
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