Automorphisms of Partially Commutative Groups I: Linear Subgroups

Details Automorphisms of Partially Commutative Groups I: Linear Subgroups Automorphisms of Partially Commutative Groups I: Linear Subgroups

2008-03-14

arxiv.org/abs/0803.2213v1

Mathematics

Group Theory

24 pages, 1 figure

Scientific paper

The goal of this paper is to construct and describe certain arithmetic subgroups of the automorphism group of a partially commutative group. More precisely, given an arbitrary finite graph $\Gamma$ we construct an arithmetic subgroup $St(L(G))$, represented as a subgroup of $GL(n,Z)$, where $n$ is the number of vertices of the graph $\Gamma$. In the last section of the paper we give a description of the decomposition of the group of automorphisms $St^{conj}(L(G))$ as a semidirect product of the group of conjugating automorphisms $Conj(G)$ and $St(L(G))$. This result is closely related to Theorem 1.4 of the paper arXiv:0710.2573v1.

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