The orthogonal group over a local ring is \(4\)-reflectional
type: Item
instance of: scholarly article
title: The orthogonal group over a local ring is \(4\)-reflectional
zbMATH Open document ID: 0801.20025
DOI: 10.1007/BF01264035
author: Hans Röpcke
published in: Geometriae Dedicata
publication date: 1994-11-21T00:00:00Z
review text: Let \(R\) be a commutative local ring such that 2 is a unit in \(R\). The author shows that every element in the orthogonal group of a free \(R\)- module of finite rank is a product of two involutions in that group. For a cyclic isometry the involutions are constructed directly. This, combined with the bireflectionality of an orthogonal group for a vector space, produces the desired result.
Mathematics Subject Classification ID: 20H25
Mathematics Subject Classification ID: 15B33
Mathematics Subject Classification ID: 20F05
Mathematics Subject Classification ID: 20G35
zbMATH DE Number: 569274
zbMATH Keywords: product of involutions
zbMATH Keywords: commutative local ring
zbMATH Keywords: orthogonal group
zbMATH Keywords: free \(R\)-module of finite rank
zbMATH Keywords: cyclic isometry
zbMATH Keywords: bireflectionality
reviewed by: Erich W. Ellers
MaRDI profile type: Publication
cites work: Q4115312
cites work: Bireflectionality of the orthogonal group over a valuation domain
cites work: Isometrien von Vektorräumen. I
cites work: Q3785040
cites work: 5-reflectionality of anisotropic orthogonal groups over valuation rings
cites work: Commutators and companion matrices over rings of stable rank 1
cites work: Q5553361
description: scientific article; zbMATH DE number 569274