The image of the automorphism group of a graph group under the abelianization map
Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 2, pp. 83-102 Cet article a éte moissonné depuis la source Math-Net.Ru

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We consider “graph-groups”, i. e. groups given by genetic codes, containing only commutativity relations for certain pairs of generators. The image of the automorphism group of a graph-group under abelianization map is described.
Keywords: graph group, link digraph, algebraic $\mathbb Q$-group, Levy decomposition, reductive group, arithmetic group, Kazhdan's property $(T)$, Serre's property $(FA)$
Mots-clés : unipotent radical, automorphism group.
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G. A. Noskov. The image of the automorphism group of a graph group under the abelianization map. Sibirskij žurnal čistoj i prikladnoj matematiki, Tome 12 (2012) no. 2, pp. 83-102. http://geodesic.mathdoc.fr/item/VNGU_2012_12_2_a7/

[1] Bestvina M., Brady N., “Morse Theory and FinitenessProperties for Groups”, Invent. Math., 129 (1997), 445–470 | DOI | MR | Zbl

[2] Croke C., Kleiner B., “Spaces with Nonpositive Curvature and Their Ideal Boundaries”, Topology, 39 (2000), 549–556 | DOI | MR | Zbl

[3] Abrams A., “Configuration Spaces of Colored Graphs”, Dedicated to John Stallings on the Occasion of His $65^\text{th}$ Birthday, Geom. Dedicata, 92 (2002), 185–194 | DOI | MR | Zbl

[4] Ghrist R., Peterson V., “The Geometry and Topology of Reconfiguration”, Adv. in Applied Mathematics, 38 (2007), 302–323 | DOI | MR | Zbl

[5] Diekert V., “Partial Commutation and Traces”, Beyond Words, Handbook of Formal Languages, 3, Springer, Heidelberg, 1997, 457–533 | DOI | MR

[6] Charney R., “An Introduction to Right-Angled Artin Groups”, Geometriae Dedicata, 125 (2007), 141–158 | DOI | MR | Zbl

[7] Van der Lek H., The Homotopy Type of Complex Hyperplane Complements, Nijmegen, 1993

[8] Servatius H., “Automorphisms of Graph Groups”, J. Algebra, 126 (1989), 34–60 | DOI | MR | Zbl

[9] Laurence M. R., “A Generating Set for the Automorphism Group of a Graph Group”, J. London Math. Soc., 52:2 (1995), 318–334 | DOI | MR | Zbl

[10] Duncan A. J., Kazachkov I. V., Remeslennikov V. N., “Automorphisms of Partially Commutative Groups I: Linear Subgroups”, Groups, Geometry, and Dynamics, 4 (2010), 739–757 | DOI | MR | Zbl

[11] Charney R., Vogtmann K., Automorphisms of Higher-Dimensional Right-Angled Artin Group, Preprint, 3 Jul 2008, arXiv: 0709.2700v2[math.GR]

[12] Grunewald F., Lubotzky A., “Linear Representations of the Automorphism Group of a Free Group”, Geometric and Functional Analysis, 18 (2009), 1564–1608 | DOI | MR | Zbl

[13] Treier A. V., Gruppy avtomorfizmov chastichno kommutativnykh 2-stupenno nilpotentnykh grupp, Dis. $\dots$ kand. fiz.-mat. nauk, Omsk, 2008

[14] Merzlyakov Yu. I., Ratsionalnye gruppy, Nauka, M., 1987 | MR | Zbl

[15] Kargopolov M. I., Merzlyakov Yu. I., Osnovy teorii grupp, 3-e izd., Nauka, M., 1982 | MR

[16] Platonov V., Rapinchuk A., Algebraic Groups and Number Theory, Academic Press, Boston, 1994 | MR | Zbl

[17] Humphreys J. E., Arithmetic Groups, Lecture Notes in Math., 789, Springer-Verlag, 1980 | MR | Zbl

[18] Culler M., Vogtmann K., “A Group-Theoretic Criterion for Property FA”, Proc. Amer. Math. Soc., 124 (1996), 677–683 | DOI | MR | Zbl

[19] Noskov G. A., “Svoistva $\mathcal T$, $\mathcal{FA}$, amenabelnost i razryvnost dlya grupp, deistvuyuschikh na $\mathbb R$-derevyakh”, Algebra i analiz, 5:3 (1993), 238–251 | MR | Zbl

[20] McCool J., “A Faithful Polynomial Representation of $Out(F_3)$”, Math. Proc. Cambridge Philos. Soc., 106 (1989), 207–213 | DOI | MR | Zbl

[21] Lyndon R. C., Schupp P. E., Combinatorial Group Theory, Springer Ergebinsberichte, 89, Berlin–Heidelberg–N.Y., 1977 | MR | Zbl

[22] Bridson M. R., Vogtmann K., “Automorphism Groups of Free Groups, Surface Groups and Free Abelian Groups”, Problems on Mapping Class Groups, Proc. of Symposia in Pure Mathematics, 74, ed. B. Farb, Providence, RI, 2006, 301–316 | DOI | MR | Zbl