Minimal generating sets in groups of ρ-automata

For an arbitrary odd prime p, we consider groups of all p-automata and all finite p-automata. We construct minimal generating sets in both the groups of all p-automata and its subgroup of finite p-automata. The key ingredient of the proof is the lifting technique, which allows the construction of a minimal generating set in a group provided a minimal generating set in its abelian quotient is given. To find the required quotient, the elements of the groups of p-automata and finite p-automata are presented in terms of tableaux introduced by L. Kaloujnine. Using this presentation, a natural homomorphism on the additive group of all infinite sequences over the field Zp is defined and examined.