Abstract
The aim of this work is to generalize nilpotent Lie superalgebras of a very important type, i.e. filiform Lie superalgebras, obtaining the notion of filiform color Lie superalgebras. We have proved the existence of an adapted basis for any G -grading of the filiform color superalgebras. Also we have proved that in order to obtain the whole class of filiform G -color Lie superalgebras it is only necessary to determine the infinitesimal deformations of the associated model color superalgebra.
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