Constructively presented projective planes
type: Item
instance of: scholarly article
title: Constructively presented projective planes
zbMATH Open document ID: 0734.51002
DOI: 10.1007/BF00147308
author: V. V. Vdovin
published in: Geometriae Dedicata
publication date: 1991-01-01T00:00:00Z
review text: In an earlier paper [Commun. Algebra 16, No.11, 2209-2230 (1988; Zbl 0654.51002)] the author has given a finite presentation for projective planes by analogy to finitely presented groups. In this article he gives another definition for a presentation of projective planes: constructively presented planes \(<X/S,A>\). It is uniquely determined by a finite set of generating symbols X and a finite set of relations S, and by a choice algorithm A. The author shows that any finitely presented projective plane may be constructively finitely presented. In particular an example is given of constructively presented planes with nonsolvable word problem. Consequently the class of all constructively finitely presented planes is larger than the class of all finitely presented planes, because any finitely presented plane has a solvable word problem.
Mathematics Subject Classification ID: 51A05
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 51A10
zbMATH DE Number: 4214815
zbMATH Keywords: finite presentation for projective planes
zbMATH Keywords: constructively presented planes
zbMATH Keywords: word problem
reviewed by: Erhard Quaisser
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4214815