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A presentation for the subgroup of compressed conjugating automorphisms of a partially commutative group | ||
| International Journal of Group Theory | ||
| مقاله 4، دوره 8، شماره 3، آذر 2019، صفحه 33-42 اصل مقاله (220.05 K) | ||
| نوع مقاله: Research Paper | ||
| شناسه دیجیتال (DOI): 10.22108/ijgt.2018.104745.1437 | ||
| نویسندگان | ||
| Abdulsatar AL-Juburie؛ Andrew Duncan* | ||
| Newcastle University | ||
| چکیده | ||
| Let $G_{\Gamma}$ be a partially commutative group. We find a finite presentation for the subgroup $Conj_v(G_{\Gamma})$ of compressed vertex conjugating automorphisms of the automorphism group $Aut(G_{\Gamma})$ of $G$. We have written GAP packages which compute presentations for $Aut(G_{\Gamma})$ and its subgroups $Conj(G_{\Gamma})$ and $Conj_v(G_{\Gamma})$. | ||
| کلیدواژهها | ||
| Partially commutative groups؛ Right-angled Artin groups؛ Automorphisms of groups | ||
| مراجع | ||
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1. A. J. AL-Juburie, Partial ly commutative and differential graded algebraic structures , Ph. D. thesis, Scho ol of Math- ematics and Statistics, Newcastle University, United Kingdom, 2015, available at https://theses.ncl.ac.uk/ . 2. A. J. AL-Juburie, A. Duncan, M. Fisher and G. Mitchell, AutParCommGrp package (Finite Presentations of Auto- morphism Groups of Partial ly Commutative Groups and Their Subgroups) , (GAP system library free software), To app ear. 3. R. Charney, An intro duction to right-angled Artin groups, Geom. Dedicata , 125 (2007) 141{158. 4. R. Charney, N. Stambaugh and K. Vogtmann, Outer space for untwisted automorphisms of right-angled Artin groups , ArXiv e-prints, (2012) 1{35. 5. M. B. Day, Peak reduction and nite presentations for automorphism groups of right-angled Artin groups, Geom. Topol. , 13 (2009) 817{855. 6. V. Diekert and G. Rozenb erg, The book of traces , World Scienti c, 1995. 7. A. J. Duncan and V. N. Remeslennikov, Automorphisms of partially commutative groups I I: Combinatorial sub- groups, Internat. J. Algebra Comput. , 22 (2012) pp. 44. 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. 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. 11. J. McCo ol, On basis-conjugating automorphisms of free groups, Canadian J. Math. , 38 (1986) 1525{1529. 12. G. A. Noskov, The image of the automorphism group of a graph group under ab elianization map, Vestnik NGU, Mat. Mekh. , 12 (2012) 83{102. 13. H. Servatius, Automorphisms of graph groups, J. Algebra , 126 (1989) 34{60. 14. E. Toinet, A nitely presented subgroup of the automorphism group of a right-angled Artin group, J. Group Theory , 15 (2012) 811{822. 15. D. T. Wise, From riches to raags: 3-manifolds, right-angled artin groups, and cubical geometry , Conference b oard of the Mathematical Sciences. Regional conference series in mathematics, American Mathematical So ciety, 2012. | ||
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