# Groups and monoids of Pythagorean triples connected to conics

Nadir Murru; Marco Abrate; Stefano Barbero; Umberto Cerruti

Open Mathematics (2017)

- Volume: 15, Issue: 1, page 1323-1331
- ISSN: 2391-5455

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topNadir Murru, et al. "Groups and monoids of Pythagorean triples connected to conics." Open Mathematics 15.1 (2017): 1323-1331. <http://eudml.org/doc/288279>.

@article{NadirMurru2017,

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 × 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.},

author = {Nadir Murru, Marco Abrate, Stefano Barbero, Umberto Cerruti},

journal = {Open Mathematics},

keywords = {Conics; Pythagorean groups; Pythagorean monoids; Pythagorean triples; Pythagorean triple preserving matrices},

language = {eng},

number = {1},

pages = {1323-1331},

title = {Groups and monoids of Pythagorean triples connected to conics},

url = {http://eudml.org/doc/288279},

volume = {15},

year = {2017},

}

TY - JOUR

AU - Nadir Murru

AU - Marco Abrate

AU - Stefano Barbero

AU - Umberto Cerruti

TI - Groups and monoids of Pythagorean triples connected to conics

JO - Open Mathematics

PY - 2017

VL - 15

IS - 1

SP - 1323

EP - 1331

AB - 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 × 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.

LA - eng

KW - Conics; Pythagorean groups; Pythagorean monoids; Pythagorean triples; Pythagorean triple preserving matrices

UR - http://eudml.org/doc/288279

ER -

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