On conjectures of andrews and curtis

Research output: Contribution to journalArticlepeer-review


It is shown that the original Andrews–Curtis conjecture on balanced presentations of the trivial group is equivalent to its “cyclic” version in which, in place of arbitrary conjugations, one can use only cyclic permutations. This, in particular, proves a satellite conjecture of Andrews and Curtis [Amer. Math. Monthly 73 (1966), 21–28]. We also consider a more restrictive “cancellative” version of the cyclic Andrews–Curtis conjecture with and without stabilizations and show that the restriction does not change the Andrews– Curtis conjecture when stabilizations are allowed. On the other hand, the restriction makes the conjecture false when stabilizations are not allowed.

Original languageEnglish (US)
Pages (from-to)2283-2298
Number of pages16
JournalProceedings of the American Mathematical Society
Issue number6
StatePublished - 2018

ASJC Scopus subject areas

  • General Mathematics
  • Applied Mathematics


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