The main objective of the present Project is to address how to set axioms tornestablish a perpendicularity relation in Abelian Group and then study thernexistence of perpendicularity in(Zn; +) and (Q+; :) in certain other groups.rnThis approach provides a justi_cation for the use of the symbol ? denotingrnrelative primeness in number theory and extends the domain of this con-rnvention to some degree.Related to that we also consider parallelism from anrnaxiomatic perspective.