Automorphisms of partially commutative groups I: Linear subgroups

  • Andrew J. Duncan

    University of Newcastle, Great Britain
  • Ilya Kazachkov

    McGill University, Montreal, Canada
  • Vladimir N. Remeslennikov

    Omsk State University, Russian Federation


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