Automorphisms of partially commutative groups I: Linear subgroups
Andrew J. Duncan
University of Newcastle, Great BritainIlya Kazachkov
McGill University, Montreal, CanadaVladimir N. Remeslennikov
Omsk State University, Russian Federation
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Abstract
We construct and describe several arithmetic subgroups of the automorphism group of a partially commutative group. More precisely, given an arbitrary finite graph we construct arithmetic subgroups and , represented as subgroups of , where is the number of vertices of the graph . Here and are certain lattices of subsets of and is the stabiliser of the subgroup generated by . In addition we give a description of the decomposition of the group , which stabilises up to conjugacy, as a semidirect product of the group of conjugating automorphisms and .
Cite this article
Andrew J. Duncan, Ilya Kazachkov, Vladimir N. Remeslennikov, Automorphisms of partially commutative groups I: Linear subgroups. Groups Geom. Dyn. 4 (2010), no. 4, pp. 739–757
DOI 10.4171/GGD/103