Quadratic isometric functions of the Heisenberg groups. A combinatorial proof
type: Item
instance of: scholarly article
title: Quadratic isometric functions of the Heisenberg groups. A combinatorial proof
zbMATH Open document ID: 0941.20034
DOI: 10.1007/BF02366347
published in: Journal of Mathematical Sciences (New York)
publication date: 1999-08-16T00:00:00Z
review text: It is presented a completely combinatorial proof of the theorem: The 5-dimensional Heisenberg group \({\mathcal H}^5=\langle x,y,u,v\mid[x,u]=[x,v]=[y,u]=[y,v]=[x,y][v,u]=1\rangle\) has a quadratic isoperimetric function. This theorem and its proof can be easily extended to any Heisenberg group \({\mathcal H}^{2n+1}\) with \(n\geq 2\) and to some other 2-nilpotent groups which are central products.
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20F65
Mathematics Subject Classification ID: 20F10
Mathematics Subject Classification ID: 22E25
Mathematics Subject Classification ID: 20F18
zbMATH DE Number: 1315226
zbMATH Keywords: Heisenberg groups
zbMATH Keywords: quadratic isoperimetric functions
zbMATH Keywords: 2-nilpotent groups
zbMATH Keywords: central products
author: Alexander Y. Olshanskii
author: Mark Sapir
reviewed by: Milica Stojanović
MaRDI profile type: Publication
cites work: An isoperimetric inequality for the Heisenberg groups
cites work: Q4003861
cites work: Q3772406
cites work: Q3140233
cites work: HYPERBOLICITY OF GROUPS WITH SUBQUADRATIC ISOPERIMETRIC INEQUALITY
full work available at URL: https://doi.org/10.1007/bf02366347
OpenAlex ID: W2042345161
description: scientific article; zbMATH DE number 1315226