Bekele, Berhanu (PhD)Bayafers, Habtu2018-07-162023-11-042018-07-162023-11-042014-08http://etd.aau.edu.et/handle/123456789/8696The main objective of the present Project is to address how to set axioms to establish a perpendicularity relation in Abelian Group and then study the existence of perpendicularity in(Zn; +) and (Q+; :) in certain other groups. This approach provides a justi_cation for the use of the symbol ? denoting relative primeness in number theory and extends the domain of this con- vention to some degree.Related to that we also consider parallelism from an axiomatic perspective.enperpendicu- larityThesis