Automorphisms of Partially Commutative Groups I: Linear Subgroups
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 March 2008
 DOI:
 10.48550/arXiv.0803.2213
 arXiv:
 arXiv:0803.2213
 Bibcode:
 2008arXiv0803.2213D
 Keywords:

 Mathematics  Group Theory;
 20E36;
 20E36;
 20F65
 EPrint:
 24 pages, 1 figure