On torsion-free groups with finite regular file bases

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

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

References in corpus (1)

• Diagrams with Selection and Method for Constructing Boundedly Generated and Boundedly Simple Groups

Cited by in corpus (1)

• Finitely generated infinite simple groups of infinite commutator width