- journal article metadata
European Mathematical Society Publishing House
2016-09-19 17:04:59
Groups, Geometry, and Dynamics
Groups Geom. Dyn.
GGD
1661-7207
1661-7215
Group theory and generalizations
10.4171/GGD
http://www.ems-ph.org/doi/10.4171/GGD
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European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society
4
2010
4
Automorphisms of partially commutative groups I: Linear subgroups
Andrew
Duncan
University of Newcastle, NEWCASTLE UPON TYNE, GREAT BRITAIN
Ilya
Kazachkov
McGill University, MONTREAL, CANADA
Vladimir
Remeslennikov
Omsk State University, OMSK, RUSSIAN FEDERATION
Partially commutative groups, right-angled Artin groups, automorphism groups, arithmetic groups
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).
Group theory and generalizations
General
739
757
10.4171/GGD/103
http://www.ems-ph.org/doi/10.4171/GGD/103