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

Full text not available from this repository.## 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 |
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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: | 15 Jan 2022 00:36 |

URI: | http://repository.essex.ac.uk/id/eprint/1804 |

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