On torsion-free groups with finite regular file bases

Author:
Alexey Muranov

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

Published electronically:
March 7, 2007

MathSciNet review:
2302509

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: The following question was asked by V. V. Bludov in The Kourovka Notebook in 1995: If a torsion-free group has a finite system of generators , ..., such that every element of has a unique presentation in the form where , is it true that is virtually polycyclic? The answer is ``not always.'' A counterexample is constructed in this paper as a group presented by generators and defining relations.

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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

DOI:
https://doi.org/10.1090/S0002-9947-07-04256-0

Keywords:
Group presentation,
van Kampen's lemma,
diagram with selection,
S-diagram,
virtually polycyclic group,
boundedly generated group,
file basis

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.

Article copyright:
© Copyright 2007
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication.