  Using concepts of physics of elementary particles concerning the breaking of
symmetry and grannd unified theory we propose to study with the algebraic
approximation the degeneracy finded in the genetic code with the incorporation
of a horizontal symmetry used in gauge theories to fit the contents of the
multiplets of the genetic code. It is used the algebraic approch of Hornos et.
al. \cite{main,PRL71,PRE,MPLB}. We propose an example for the incorporation of
horizontal symmetry to study mixtures of elements of the multiplets.
