The groups of $ZC$-automaton transformations

Under study are the $ZC$-automata and the transformation groups determined by them. We establish relationships between the group of $ZC$-automaton transformations and the group of infinite unitriangular integer matrices. We describe the derived series of the group of $ZC$-automaton transformations and present conditions for the representability of residually solvable groups by $ZC$-automaton transformations. We construct a continual family of $ZC$-automata with two states, each of which generates a free semigroup.