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arXiv · 1712.08812

Groups and monoids of Pythagorean triples connected to conics

Marco Abrate·Stefano Barbero·Umberto Cerruti·Nadir Murru
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Abstract

We define operations that give the set of all Pythagorean triples a structure of commutative monoid. In particular, we define these operations by using injections between integer triples and $3 \times 3$ matrices. Firstly, we completely characterize these injections that yield commutative monoids of integer triples. Secondly, we determine commutative monoids of Pythagorean triples characterizing some Pythagorean triple preserving matrices. Moreover, this study offers unexpectedly an original connection with groups over conics. Using this connection, we determine groups composed by Pythagorean triples with the studied operations.

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Marco Abrate, Stefano Barbero, Umberto Cerruti, Nadir Murru. 2017-12-23. Groups and monoids of Pythagorean triples connected to conics. https://arxiv.org/abs/1712.08812

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