On torsion-free groups with finite regular file bases

Details On torsion-free groups with finite regular file bases On torsion-free groups with finite regular file bases

2005-04-21

arxiv.org/abs/math/0504438v3

Trans. Amer. Math. Soc. 359 (2007), no. 8, 3609--3645

Mathematics

Group Theory

version 3: 40 pages, 12 figures, typos corrected, converted to LaTeX; v2: 38 pages, 12 figures, improved readability; v1: 40 p

Scientific paper

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 $a_1^{k_1}... a_n^{k_n}$ 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.

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