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ONE-SIDE NIELSEN TRANSFORMATIONS IN FREE GROUPS

VERNITSKI, ALEXEI (2009) 'ONE-SIDE NIELSEN TRANSFORMATIONS IN FREE GROUPS.' International Journal of Algebra and Computation, 19 (07). pp. 855-871. ISSN 0218-1967

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Abstract

<jats:p> We study a graph related to the Andrews—Curtis graph. The vertices are pairs of elements of a free group, and two vertices are adjacent if they can be obtained from one another by a left Nielsen transformation, that is, for each two words u, v the pair (u, v) is adjacent to (vu, v), (v<jats:sup>‑1</jats:sup>u, v), (u, uv), and (u, u<jats:sup>‑1</jats:sup>v). We study connected components of the graph and describe the shortest pairs in all components. Hence, we find a linear-time algorithm for checking whether two pairs belong to the same connected component of the graph. </jats:p>

Item Type: Article
Uncontrolled Keywords: Free group; Nielsen transformation; Andrews-Curtis graph; connected component; linear-time algorithm
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health
Faculty of Science and Health > Mathematical Sciences, Department of
SWORD Depositor: Elements
Depositing User: Elements
Date Deposited: 04 Jan 2012 11:17
Last Modified: 18 Aug 2022 11:13
URI: http://repository.essex.ac.uk/id/eprint/1804

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