In this work, it is considered that the vector space is composed by the infinitesimal deformations of the model Z3-filiform Lie algebra Ln,m,p. By using these deformations, all the Z3-filiform Lie algebras can be obtained, hence the importance of these deformations. The results obtained in this work, together with those obtained by Khakimdjanov and Navarro (J. Geom. Phys. 2011 and 2012), lead to compute the total dimension of the mentioned space of deformations.
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