Abstract
The purpose of this note is to show by elementary means that over the field of real numbers, or more generally over any Euclidean field K with Archimedean order the group of n -dimensional Euclidean similarities is maximal within the group of all affine mappings having a determinant of the form . As a corollary it turns out that the orthogonal group is maximal within the group of all matrices of determinant .
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