Geodesic
Automorphisms of partially commutative groups I: Linear subgroups
Andrew J. Duncan1 ; Ilya Kazachkov2 ; Vladimir N. Remeslennikov3
1University of Newcastle, Great Britain
2McGill University, Montreal, Canada
3Omsk State University, Russian Federation
Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 739-757

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DOI

We construct and describe several arithmetic subgroups of the automorphism group of a partially commutative group. More precisely, given an arbitrary finite graph Γ we construct arithmetic subgroups St(LY​) and St(Lmax), represented as subgroups of GL(n,Z), where n is the number of vertices of the graph Γ. Here LY​ and Lmax are certain lattices of subsets of X=V(Γ) and St(K) is the stabiliser of the subgroup generated by K. In addition we give a description of the decomposition of the group Stconj(LX​), which stabilises LX​ up to conjugacy, as a semidirect product of the group of conjugating automorphisms and St(LX​).
DOI : 10.4171/ggd/103
Classification : 20-XX, 00-XX
Mots-clés : Partially commutative groups, right-angled Artin groups, automorphism groups, arithmetic groups

Andrew J. Duncan  1   ; Ilya Kazachkov  2   ; Vladimir N. Remeslennikov  3

1 University of Newcastle, Great Britain
2 McGill University, Montreal, Canada
3 Omsk State University, Russian Federation 
Andrew J. Duncan; Ilya Kazachkov; Vladimir N. Remeslennikov. Automorphisms of partially commutative groups I: Linear subgroups. Groups, geometry, and dynamics, Tome 4 (2010) no. 4, pp. 739-757. doi: 10.4171/ggd/103
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     author = {Andrew J. Duncan and Ilya Kazachkov and Vladimir N. Remeslennikov},
     title = {Automorphisms of partially commutative groups {I:} {Linear} subgroups},
     journal = {Groups, geometry, and dynamics},
     pages = {739--757},
     year = {2010},
     volume = {4},
     number = {4},
     doi = {10.4171/ggd/103},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/ggd/103/}
}
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