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Groups Complexity Cryptology

Managing Editor: Shpilrain, Vladimir / Weil, Pascal

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Cyclic rewriting and conjugacy problems

Volker Diekert
  • Universität Stuttgart, Universitätsstr. 38, 70569 Stuttgart, Germany
  • Email:
/ Andrew Duncan
  • Newcastle University, Newcastle upon Tyne, NE1 7RU, UK
  • Email:
/ Alexei G. Myasnikov
  • Stevens Institute of Technology, Hoboken NJ 07030-5991, USA
  • Email:
Published Online: 2012-11-27 | DOI: https://doi.org/10.1515/gcc-2012-0020


Cyclic words are equivalence classes of cyclic permutations of ordinary words. When a group is given by a rewriting relation, a rewriting system on cyclic words is induced, which is used to construct algorithms to find minimal length elements of conjugacy classes in the group. These techniques are applied to the universal groups of Stallings pregroups and in particular to free products with amalgamation, HNN-extensions and virtually free groups, to yield simple and intuitive algorithms and proofs of conjugacy criteria.

Keywords: Algorithmic group theory; rewriting system; conjugacy problem; HNN-extension; free product with amalgamation; Stallings pregroup

About the article

Received: 2012-06-17

Published Online: 2012-11-27

Published in Print: 2012-12-01

Citation Information: , ISSN (Online) 1869-6104, ISSN (Print) 1867-1144, DOI: https://doi.org/10.1515/gcc-2012-0020. Export Citation

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