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One-side Nielsen transformations in free groups

Vernitski, A (2009) 'One-side Nielsen transformations in free groups.' International Journal of Algebra and Computation, 19 (7). 855 - 871. ISSN 0218-1967

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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-1u, v), (u, uv), and (u, u-1v). 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. © 2009 World Scientific Publishing Company.

Item Type: Article
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Science and Health > Mathematical Sciences, Department of
Depositing User: Jim Jamieson
Date Deposited: 04 Jan 2012 11:17
Last Modified: 30 Jun 2021 10:15

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