On Pythagorean Triples

We talk about pythagorean triples and their different representations, we permute these representations to form groups, we classify these groups with a quotient and find that this quotient is related to NSW numbers and primes of the form 2x 2 − y 2 , then we talk about some properties related to all groups, including a pythagorean triples generator, also we talk about linearity, recursion and periodicity, we finally talk about two specific groups and give some identities