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Automorphisms of partially commutative groups I: Linear subgroups

Lookup NU author(s): Dr Andrew Duncan, Ilia Kazatchkov, Professor Vladimir Remeslennikov

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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 Gamma we construct arithmetic subgroups St(LY) and St(L-max), represented as subgroups of GL(n, Z), where n is the number of vertices of the graph Gamma. Here L-Y and L-max are certain lattices of subsets of X = V(Gamma) and St(K) is the stabiliser of the subgroup generated by K. In addition we give a description of the decomposition of the group St(conj)(L-X), which stabilises LX up to conjugacy, as a semidirect product of the group of conjugating automorphisms and St(L-X).

Publication metadata

Author(s): Duncan AJ, Kazachkov IV, Remeslennikov VN

Publication type: Article

Publication status: Published

Journal: Groups, Geometry, and Dynamics

Year: 2010

Volume: 4

Issue: 4

Pages: 739-757

Print publication date: 01/01/2010

ISSN (print): 1661-7207

ISSN (electronic): 1661-7215

Publisher: European Mathematical Society Publishing House

URL: http://dx.doi.org/10.4171/GGD/103

DOI: 10.4171/GGD/103

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