  One may ask whether an extended group of invariance can naturally be
attributed to the space of associative commutative Quadrahyperbolic Numbers? To
search for a rigorous and positive answer to the question, we shall focus on
the method of derivation of the respective invariance. The outcome that there
exist 3--parametric nonlinear transformations which leave invariant the scalar
product chosen appropriately for The Quadrahyperbolic Numbers, is the main
result of the present publication.
