On torsion-free groups with finite regular file bases
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- by Alexey Muranov PDF
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Abstract:
The following question was asked by V. V. Bludov in The Kourovka Notebook in 1995: If a torsion-free group $G$ has a finite system of generators $a_{1}$, …, $a_{n}$ such that every element of $G$ has a unique presentation in the form $a_{1}^{k_{1}}\cdots a_{n}^{k_{n}}$ where $k_{i}\in \mathbb {Z}$, is it true that $G$ is virtually polycyclic? The answer is “not always.” A counterexample is constructed in this paper as a group presented by generators and defining relations.References
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Additional Information
- Alexey Muranov
- Affiliation: Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, Tennessee 37240–0001
- Address at time of publication: Institut Camille Jordan, Université Lyon 1, 43 blvd du 11 novembre 1918, 69622 Villeurbanne cedex, France
- Email: muranov@math.univ-lyon1.fr
- Received by editor(s): March 4, 2005
- Published electronically: March 7, 2007
- Additional Notes: This work was supported in part by the NSF grant DMS 0245600 of Alexander Ol’shanskiy and Mark Sapir.
- © Copyright 2007
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 359 (2007), 3609-3645
- MSC (2000): Primary 20F05; Secondary 20F06
- DOI: https://doi.org/10.1090/S0002-9947-07-04256-0
- MathSciNet review: 2302509