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


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.

DOI Code: 10.1285/i15900932v21n2p135

Full Text: PDF
کاغذ a4

Creative Commons License
This work is licensed under a Creative Commons Attribuzione - Non commerciale - Non opere derivate 3.0 Italia License.