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On Conjectures of Andrews and Curtis


Author: S. V. Ivanov
Journal: Proc. Amer. Math. Soc. 146 (2018), 2283-2298
MSC (2010): Primary 20F05, 20F06, 57M20
DOI: https://doi.org/10.1090/proc/13710
Published electronically: March 9, 2018
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Abstract: 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.


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Additional Information

S. V. Ivanov
Affiliation: Department of Mathematics, University of Illinois, Urbana, Illinois 61801
Email: ivanov@illinois.edu

DOI: https://doi.org/10.1090/proc/13710
Received by editor(s): August 30, 2015
Received by editor(s) in revised form: June 22, 2016
Published electronically: March 9, 2018
Additional Notes: The author was supported in part by the National Science Foundation, grant DMS 09-01782
Communicated by: Pham Huu Tiep
Article copyright: © Copyright 2018 American Mathematical Society

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