Automorphisms of Partially Commutative Groups I: Linear Subgroups

2008/03/14 by Andrew J. Duncan, Ilya V. Kazachkov, Duncan, Andrew J. +5
Mathematics · #20E36 #20F65 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Geometric and Algebraic Topology #Group Theory (math.GR) #math.GR #msc:20E36 #msc:20F65

paper · pdf · doi:10.48550/arxiv.0803.2213

24 pages, 1 figure

arxiv created 2008/03/14 · openalex publication_date 2008/03/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 Γ 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 Γ. 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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