International Journal of Mathematics and Mathematical Sciences
Volume 2013 (2013), Article ID 983607, 8 pages
http://dx.doi.org/10.1155/2013/983607
Research Article

Perpendicularity in an Abelian Group

Pentti Haukkanen,1 Mika Mattila,1 Jorma K. Merikoski,1 and Timo Tossavainen2

1School of Information Sciences, University of Tampere, 33014, Finland
2School of Applied Educational Science and Teacher Education, University of Eastern Finland, P.O. Box 86, 57101 Savonlinna, Finland

Received 12 January 2013; Accepted 19 March 2013

Academic Editor: Petru Jebelean

Copyright © 2013 Pentti Haukkanen et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We give a set of axioms to establish a perpendicularity relation in an Abelian group and then study the existence of perpendicularities in and and in certain other groups. Our approach provides a justification for the use of the symbol denoting relative primeness in number theory and extends the domain of this convention to some degree. Related to that, we also consider parallelism from an axiomatic perspective.