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Perpendicularity in an Abelian group. (English) Zbl 1264.51012
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.

MSC:
51M05 Euclidean geometries (general) and generalizations
51F20 Congruence and orthogonality in metric geometry
20K01 Finite abelian groups
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