  Due to the noncommutative nature of quaternions and octonions we introduce
barred operators. This objects give the opportunity to manipulate appropriately
the hypercomplex fields. The standard problems arising in the definitions of
transpose, determinant and trace for quaternionic and octonionic matrices are
immediately overcome. We also investigate the possibility to formulate a new
approach to Hypercomplex Group Theory (HGT). From a mathematical viewpoint, our
aim is to highlight the possibility of looking at new hypercomplex groups by
the use of barred operators as fundamental step toward a clear and complete
discussion of HGT.
