A note on small similarity groups
type: Item
instance of: scholarly article
title: A note on small similarity groups
zbMATH Open document ID: 0675.10013
DOI: 10.1007/BF01222255
author: Burkhard Alpers
published in: Journal of Geometry
publication date: 1989-01-01T00:00:00Z
review text: Let q be a nondegenerate quadratic form on \(k^ n\), where k is a field of characteristic distinct from 2. If n is odd, then every similarity factor of q is a square in k, and the similarity group GO(q) is small in the sense that \(GO(q)=k^*O(q)\). The paper contains some remarks about characterizations of this situation over various fields; e.g. if k is a formally real global field, then the similarity group is small if and only if n is odd.
Mathematics Subject Classification ID: 11E04
Mathematics Subject Classification ID: 11E12
zbMATH DE Number: 4105052
zbMATH Keywords: u-invariant
zbMATH Keywords: quadratic form
zbMATH Keywords: similarity factor
zbMATH Keywords: similarity group
zbMATH Keywords: formally real global field
MaRDI profile type: Publication
cites work: Q3797784
cites work: Quadratic forms and the u-invariant
cites work: Round and group quadratic forms over global fields
cites work: Fröhlich's local quadratic forms.
cites work: Q3663392
cites work: Q3708857
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description: scientific article; zbMATH DE number 4105052