Sikora V.S. On Systems Of Generators Of Automaton Permutation Groups // International Scientific Periodical Journal "SWorldJournal".– 2022.– Issue 11, Part 2.– P.38–44.– Published by Academy of Economics named after D.A. Tsenov (Bulgaria) jointly with SWorld.

Abstract

Systems of induced generating actions of automaton permutation groups on words of length r are investigated. A family of irreducible systemsof generators is constructed, and the cardinality of such systems is found to be related with r.The theorem is proved that arbitrary minimal (on quantity of the elements) system of generators of the (,)S nr-group consists of relements, r>=2.