A presentation for the subgroup of compressed conjugating automorphisms of a partially commutative group. (English) Zbl 1443.20060

Summary: Let \(G_\Gamma\) be a partially commutative group. We find a finite presentation for the subgroup \(\mathrm{Conj}_V (G_\Gamma)\) of compressed vertex conjugating automorphisms of the automorphism group \(\operatorname{Aut} (G_\Gamma)\) of G. We have written GAP packages which compute presentations for \(\operatorname{Aut} (G_\Gamma)\) and its subgroups \(\mathrm{Conj}(G_\Gamma)\) and \(\mathrm{Conj}_V(G_\Gamma )\).


20F28 Automorphism groups of groups
20F05 Generators, relations, and presentations of groups
20F36 Braid groups; Artin groups


GAP; AutParCommGrp
Full Text: DOI


[1] A. J. AL-Juburie,Partially commutative and differential graded algebraic structures, Ph. D. thesis, School of Mathematics and Statistics, Newcastle University, United Kingdom, 2015, available athttps://theses.ncl.ac.uk/.
[2] A. J. AL-Juburie, A. Duncan, M. Fisher and G. Mitchell,AutParCommGrp package (Finite Presentations of Automorphism Groups of Partially Commutative Groups and Their Subgroups), (GAP system library free software), To appear.
[3] R. Charney, An introduction to right-angled Artin groups,Geom. Dedicata,125(2007) 141-158. · Zbl 1152.20031
[4] R. Charney, N. Stambaugh and K. Vogtmann,Outer space for untwisted automorphisms of right-angled Artin groups, ArXiv e-prints, (2012) 1-35. · Zbl 1405.20028
[5] M. B. Day, Peak reduction and finite presentations for automorphism groups of right-angled Artin groups,Geom. Topol.,13(2009) 817-855. · Zbl 1226.20024
[6] V. Diekert and G. Rozenberg,The book of traces, World Scientific, 1995.
[7] A. J. Duncan and V. N. Remeslennikov, Automorphisms of partially commutative groups II: Combinatorial subgroups,Internat. J. Algebra Comput.,22(2012) pp. 44. · Zbl 1257.20038
[8] E. S. Esyp, I. V. Kazachkov and V. N. Remeslennikov, Divisibility theory and complexity of algorithms for free partially commutative groups,Contemp. Math., Groups, Languages, Algorithms,378(2005) 319-348. · Zbl 1160.20306
[9] The GAP Group,GAP - Groups, Algorithms, and Programming, Version 4.7.9, 2015.
[10] M. Laurence, A generating set for the automorphism group of a graph group,J. London Math. Soc.,52(1995) 318-334. · Zbl 0836.20036
[11] J. McCool, On basis-conjugating automorphisms of free groups,Canadian J. Math.,38(1986) 1525-1529. · Zbl 0613.20024
[12] G. A. Noskov, The image of the automorphism group of a graph group under abelianization map, Vestnik NGU, Mat. Mekh.,12(2012) 83-102. · Zbl 1289.20066
[13] H. Servatius, Automorphisms of graph groups,J. Algebra,126(1989) 34-60. · Zbl 0682.20022
[14] E. Toinet, A finitely presented subgroup of the automorphism group of a right-angled Artin group,J. Group Theory, 15(2012) 811-822. · Zbl 1275.20037
[15] D.
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