The Pauli principle and hidden symmetries

The consequencies of hypothesis as to the existence of Gsub(n)=Usub(n), SUsub(n), Osub(n), SOsub(n) (n >= 2) symmetry groups for particles with semi-integer spins, that obey the Fermi-Dirac statistics are considered. Possible realizations of Gsub(n) group in the four-dimensional space are the following: a) completely broken symmetry of Gsub(n) group; b) the unbroken symmetry of Gsub(n) group. Then this group should be hidden, and in a free state there can exist only scalar constructions of Gsub(n)