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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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##### References:
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