Summary: Formal groups of transformations in the space of differential and network (finite-difference) variables are considered. It is shown that conservation of the sense of difference derivatives by transformations leads with necessity to Lie-Bäcklund groups. Formulas of continuation to network variables are derived and criteria of conservation of uniformity and invariance of the difference network and criterion of invariance of difference equations are formulated.
With the help of formal Newton series, an ideal of the algebra of all Lie-Bäcklund operators on a uniform network is constructed which is used for derivation of a criterion of conservation of difference equations on the basis of the discrete analog of the Noether identity.
English translation in J. Sov. Math. 55, No. 1, 1490–1517 (1991; Zbl 0727.65074).