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An extension of the adjoint SU(5) model with a flavour symmetry based on theZ_4 group is investigated. The Z_4 symmetry is introduced with the aim ofleading the up- and down-quark mass matrices to theNearest-Neighbour-Interaction form. As a consequence of the discrete symmetryembedded in the SU(5) gauge group, the charged lepton mass matrix also gets thesame form. Within this model, light neutrinos get their masses through type-I,type-III and one-loop radiative seesaw mechanisms, implemented, respectively,via a singlet, a triplet and an octet from the adjoint fermionic 24 fields. Itis demonstrated that the neutrino phenomenology forces the introduction of atleast three 24 fermionic multiplets. The symmetry SU(5)xZ_4 allows only twoviable zero textures for the effective neutrino mass matrix. It is showed thatone texture is only compatible with normal hierarchy and the other withinverted hierarchy in the light neutrino mass spectrum. Finally, it is alsodemonstrated that Z_4 freezes out the possibility of proton decay throughexchange of colour Higgs triplets at tree-level.

The minimal adjoint-SU(5)xZ_4 GUT model