The paths of unification in the GUST with the G × G gauge groups of E(8) × E(8)

In the framework of the four dimensional heterotic superstring with free fermions we discuss the rank eight and/or sixteen Grand Unified String Theories (GUST) which contain the SU(3)H-gauge family symmetry. We explicitly investigate the paths of the unification in the GUST with gauge symmetry G × G = [SU(5) × U(1) × (SU(3) × U(1))H]⊗2. We show that the GUSTs with the G × G gauge group allow to make the scale of unification to be consistent with the string scale MSU ∼ gstring · 5 · 1017 GeV.