A note on small similarity groups
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.
scientific article; zbMATH DE number 4105052
scientific article