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arXiv · 1706.09517

Automorphisms of Partially Commutative Groups III: Inversions and Transvections

Andrew J. Duncan·Vladimir N. Remeslennikov
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Abstract

The structure of a certain subgroup $S$ of the automorphism group of a partially commutative group (RAAG) $G$ is described in detail: namely the subgroup generated by inversions and elementary transvections. We define admissible subsets of the generators of $G$, and show that $S$ is the subgroup of automorphisms which fix all subgroups $\langle Y\rangle$ of $G$, for all admissible subsets $Y$. A decomposition of $S$ as an iterated tower of semi-direct products in given and the structure of the factors of this decomposition described. The construction allows a presentation of $S$ to be computed, from the commutation graph of $G$.

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Andrew J. Duncan, Vladimir N. Remeslennikov. 2017-06-29. Automorphisms of Partially Commutative Groups III: Inversions and Transvections. https://arxiv.org/abs/1706.09517

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