# A Characterization of Those Automata That Structurally Generate Finite Groups

@article{Klimann2014ACO, title={A Characterization of Those Automata That Structurally Generate Finite Groups}, author={Ines Klimann and Matthieu Picantin}, journal={ArXiv}, year={2014}, volume={abs/1310.7137} }

Antonenko and Russyev independently have shown that any Mealy automaton with no cycles with exit--that is, where every cycle in the underlying directed graph is a sink component--generates a fi- nite (semi)group, regardless of the choice of the production functions. Antonenko has proved that this constitutes a characterization in the non-invertible case and asked for the invertible case, which is proved in this paper.

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## Iterating Transducers

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