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The system of equations describing 4 generations with thesymmetry group $SU(3)_{C}\times SU(2)_{L}\timesU(1) 1 Belarus State University of Informatics and Radioelectronics Academic Editor: Eduardo Guendelman https://doi.org/10.3390/Symmetry2021-10725 (registering DOI) Abstract: The system of 16-component equations including two equations of the Bethe-Salpeter kind (without an interaction) and two additional conditions are considered. It is shown that the group of the initial symmetry is$SU(3)_{C}\times SU(2)_{L}\times
U(1)$. The symmetry group is established as the consequence of the field equations;$ SU(2)$should be chiral, the color space has the signature$ (++-)$. The structure of permissible multiplets of the group coincides with the one postulated in the$SU(3)_{C}\times SU(2)_{L}$-model of strong and electroweak interactions excluding the possible existence of the additional$SU(2)_{R}
\$-singlet in a generation. It is shown here that at least three puzzling features of the
standard model: the existence of a few generations, the specific
symmetry group, and the necessity to use its interwoven
representations may originate from the composite nature of the
fundamental fermions. \footnote{This paper (in Russian) was deposited in VINITY
19.12.1988 as VINITI No 8842-B88; it was an important stage in the
development of my model of the composite fundamental fermions (see
hep-th/0207210). Now I have translated it in English (small
corrections are made) to do more available.}

Keywords: composite fundamental fermions