The Maximality of the Group of Euclidean Similarities within the Affine Group II

Authors

  • Adolf Schleiermacher
  • Karl Strambach

DOI:

https://doi.org/10.1285/i15900932v21n2p135

Abstract

The purpose of this note is to show that for an arbitrary Pythagorean field $K$ the group $O^+_n(K)$ is maximal within $SL_n(K)$ if, and only if, $K$ admits only of Archimedean orderings.Under the same conditions the group of $n-$dimensional Euclidean similarities is maximal within the group of all affine mappings having a determinant of the form $\pm\lambda^n \not=0$.

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Published

01-06-2002

Issue

Volume 21, Issue 2 (2002)

Section

Articoli

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