ON THE GROUP OF ISOMETRIES OF THE PLANE WITH GENERALIZED ABSOLUTE VALUE METRIC

Kaya R., GELİŞGEN Ö., Ekmekci S., Bayar A.

ROCKY MOUNTAIN JOURNAL OF MATHEMATICS, vol.39, no.2, pp.591-603, 2009 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 39 Issue: 2
  • Publication Date: 2009
  • Doi Number: 10.1216/rmj-2009-39-2-591
  • Journal Name: ROCKY MOUNTAIN JOURNAL OF MATHEMATICS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.591-603
  • Keywords: Isometry, distance, metric, taxicab distance, Chinese checkers metric, dihedral group, symmetry groups
  • Eskisehir Osmangazi University Affiliated: Yes

Abstract

In this work, we show that the group of isometries of the plane with generalized absolute value metric is either the semi-direct product of the group D-4 and T(2) or the semi-direct product of the Dihedral group D-8 and T(2) where D-4 and D-8 are the (Euclidean) symmetry groups of the square and the regular octagon, respectively; and T(2) is the group of all translations of the plane.