 After Grigorchuk's 1984 paper, there were many subsequent extensions and generalizations.Although initially the Grigorchuk group was defined as a group of Lebesgue measure-preserving transformations of the unit interval, at present this group is usually given by its realization as a group of automorphisms of the infinite regular binary rooted tree "T"2.The tree "T"2 is realized as the set formula_8 of all finite strings in the alphabet formula_9 plus the empty string formula_10 which is the root vertex of "T"2.