… automaton (s) need to be used as generators) is justified by the self-similarity structure that is
apparent as soon as a group is realized as an automaton group… The symmetric group Sym (…

… permutation groups are associated with any finite monogenic automaton A, namely the
Suschkewitsch group … > will denote a finite monogenic automaton, S the set of generators of A (ie …

For a group G and a finite set A, denote by $$\mathrm {CA}(G;A)$$ the monoid of all cellular
automata over $$A^G$$ and by $$\mathrm {ICA}(G;A)$$ its group of units. We study the …

… automaton A, is a permutation if and only if the automaton A … The group F GA(X) can be
constructed of symmetric groups … not know any not very excessive system of generators of F GA(X)…

… Suppose we are given generators g1,...,gn of a permutation group. Form a directed graph
with edges (x,xgi) for all x ∈ Ω … How do we recognise when an automaton is synchronizing? …

… group elements; and the automaton Ms recognizes when two such singled out words represent
group elements differing by a generator. … the symmetric group of A (acting by permutation …

… Composition of functions is from right to left and all groups (including permutation groups) …
Combining the previous lemma with any standard set of generators for Alt(A2), we obtain a set …

… vertices by elements of the symmetric group Sn of degree n (… a power of a fixed cyclic
permutation & of the set of n edges. … , the automaton N describes the labelling for generators a, ẞ …

… , we may mention the transformation semigroups and permutation groups of sets. Let N be a
… of the generator algebras, the proof of Theorem 3.2 follows from the inclusion G = HSP({A}). …

… for such groups. We describe the sufficient condition for an essentially free automaton group
to … A Mihailova normal form of the group H is a system of generators {s1,...,sn,u1,...,um} of H …