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Automorphism of partially commutative groups II: Combinatorial subgroups

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

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Abstract

We define several "standard" subgroups of the automorphism group Aut(G) of a partially commutative (right-angled Artin) group and use these standard subgroups to describe decompositions of Aut(G). If C is the commutation graph of G, we show how Aut(G) decomposes in terms of the connected components of C: obtaining a particularly clear decomposition theorem in the special case where C has no isolated vertices. If C has no vertices of a type we call dominated then we give a semi-direct decomposition of Aut(G) into a subgroup of locally conjugating automorphisms by the subgroup stabilizing a certain lattice of "admissible subsets" of the vertices of C. We then characterize those graphs for which Aut(G) is a product (not necessarily semi-direct) of two such subgroups.

Publication metadata

Author(s): Duncan AJ, Remeslennikov VN

Publication type: Article

Publication status: Published

Journal: International Journal of Algebra and Computation

Year: 2012

Volume: 22

Issue: 7

Print publication date: 28/11/2012

ISSN (print): 0218-1967

ISSN (electronic): 1793-6500

Publisher: World Scientific Publishing Co. Pte. Ltd.

URL: http://dx.doi.org/10.1142/S0218196712500749

DOI: 10.1142/S0218196712500749

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