Free product Z3*Z3 of rotations with rational entries Original Research Article

In this paper we develop an approach to constructing the free product Z3*Z3 of rotations which avoids transcendental numbers and irrational numbers. The main result is that two rotations of order three g and h with rational entries generate the free product Z3*Z3 if (gh)2not identical with0 (mod p), when appropriate p-divisibility conditions are satisfied for integer vectors that yield quaternion covers.