File bases in groups
type: Item
instance of: scholarly article
title: File bases in groups
zbMATH Open document ID: 0854.20040
DOI: 10.1007/BF02341869
author: V. V. Bludov
published in: Algebra and Logic
publication date: 1997-01-21T00:00:00Z
full work available at URL: https://eudml.org/doc/187723
review text: The author defines file bases as special systems of generators of a group \(G\) in which every element of \(G\) has a unique representation of a special form. A lot of examples of groups which have file bases are represented. It is proved that the class of groups which have file bases is closed under extensions, direct and free products. With some natural restrictions it is shown that the quotient \(G/H\) has a file basis if a group \(G\) has it. Some open questions on groups with file bases are formulated.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20E34
zbMATH DE Number: 907266
zbMATH Keywords: Mal'tsev bases
zbMATH Keywords: nilpotent groups
zbMATH Keywords: free groups
zbMATH Keywords: file bases
zbMATH Keywords: systems of generators
zbMATH Keywords: free products
MaRDI profile type: Publication
cites work: Q4745979
cites work: Relatively convex subgroups of orderable groups
cites work: Q3691723
description: scientific article; zbMATH DE number 907266