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The notions of tensor end exterior products moduloq of two crossed P-modules, where q is a positive integer and P is a Lie algebra, are introduced and some properties are established. The condition for the existence of a universal q-central relative extension of a Lie epimorphism is given and this extension is described as an exterior product modulo q.

Non-abelian tensor and exterior products modulo $q$ and universal $q$-central relative extension of Lie algebras