On Rourke's extension of group presentations and a cyclic version of the andrews-curtis conjecture

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Abstract

In 1979, Rourke proposed to extend the set of cyclically reduced defining words of a group presentation P by using operations of cyclic permutation, inversion and taking double products. He proved that iterations of these operations yield all cyclically reduced words of the normal closure of defining words of 7 if the group, defined by the presentation 7, is trivial. We generalize this result by proving it for every group presentation 7 with an obvious exception. We also introduce a new, "cyclic", version of the Andrews-Curtis conjecture and show that the original Andrews-Curtis conjecture with stabilizations is equivalent to its cyclic version.

Original languageEnglish (US)
Pages (from-to)1561-1567
Number of pages7
JournalProceedings of the American Mathematical Society
Volume134
Issue number6
DOIs
StatePublished - Jun 2006

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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