2017/08/23 by Olukoya, Feyishayo
#20E08 (Secondary) #68Q45 (Primary) #FOS: Mathematics #Group Theory (math.GR)
paper · doi:10.48550/arxiv.1708.07209
We give sufficient conditions for when groups generated by automata in a class C of transducers, which contains the class of reset automata transducers, have infinite order. As a consequence we also demonstrate that if a group generated by an automata in C is infinite, then it contains a free semigroup of rank at least 2. This gives a new proof, in the context of groups generated by automaton in C, of a result of Chou showing that finitely generated elementary amenable groups either have polynomial growth or contain a free semigroup of rank at least 2.