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


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.

DOI Code: 10.1285/i15900932v21n2p135

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