In this paper we describe solvable Leibniz algebras whose quotient algebra by one-dimensional ideal is a Lie algebra with rank equal to the length of the characteristic sequence of its nilpotent radical. We prove that such Leibniz algebra is unique and centerless. Also it is proved that the first and the second cohomology groups of the algebra with coefficients in itself is trivial.

The paper is devoted to the study of pro-solvable Lie algebras whose maximal pronilpotent ideal is either m 0 or m 2 . Namely, we describe such Lie algebras and establish their completeness. Triviality of the second cohomology group for one of the obtained algebra is established.

In the paper the class of all solvable extensions of a filiform Leibniz algebra in the infinitedimensional case is classified. The filiform Leibniz algebra is taken as a maximal pro-nilpotent ideal of residually solvable Leibniz algebra. It is proven that the second cohomology group of the extension is trivial.

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