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Automorphisms of partially commutative groups III: Inversions and transvections

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

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Abstract

© 2018 World Scientific Publishing Company The automorphism group of a partially commutative group (Formula presented.) is generated by four types of automorphism: graph automorphisms, inversions, transvections and vertex conjugating automorphisms. We find a characterisation of the subgroup (Formula presented.) generated by inversions and transvections, in terms of stabilisers of subgroups of (Formula presented.) generated by the so-called “admissible” subsets of (Formula presented.). This is used to give a decomposition of (Formula presented.) as a chain of semi-direct products of (mostly) tractable and recognisable subgroups; which in turn gives rise to a presentation of (Formula presented.).

Publication metadata

Author(s): Duncan AJ, Remeslennikov VN

Publication type: Article

Publication status: Published

Journal: International Journal of Algebra and Computation

Year: 2018

Volume: 28

Issue: 6

Pages: 1017-1047

Print publication date: 01/09/2018

Online publication date: 11/07/2018

Acceptance date: 30/05/2018

ISSN (print): 0218-1967

ISSN (electronic): 1793-6500

Publisher: World Scientific Publishing Co. Pte Ltd

URL: https://doi.org/10.1142/S0218196718500455

DOI: 10.1142/S0218196718500455

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