On torsion-free groups with finite regular file bases期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On torsion-free groups with finite regular file bases

Authors:	Alexey Muranov

Affiliation:	Department of Mathematics, Vanderbilt University, 1326 Stevenson Center, Nashville, Tennessee 37240--0001

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 $a_{1}$ , ..., $a_{n}$ such that every element of 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 is virtually polycyclic? The answer is ``not always.' A counterexample is constructed in this paper as a group presented by generators and defining relations.

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

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