Perpendicularity in an Abelian group (Q1950027)

Summary: We give a set of axioms to establish a perpendicularity relation in an abelian group and then study the existence of perpendicularities in \((\mathbb Z_n, +)\) and \((\mathbb Q_+, \cdot)\) and in certain other groups. Our approach provides a justification for the use of the symbol \(\perp\) 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.