A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group
نویسندگان
چکیده
منابع مشابه
A Connected 3-State Reversible Mealy Automaton Cannot Generate an Infinite Burnside Group
The class of automaton groups is a rich source of the simplest examples of infinite Burnside groups. However, there are some classes of automata that do not contain such examples. For instance, all infinite Burnside automaton groups in the literature are generated by non reversible Mealy automata and it was recently shown that 2-state invertible-reversible Mealy automata cannot generate infinit...
متن کاملConnected Reversible Mealy Automata of Prime Size Cannot Generate Infinite Burnside Groups
The simplest example of an infinite Burnside group arises in the class of automaton groups. However there is no known example of such a group generated by a reversible Mealy automaton. It has been proved that, for a connected automaton of size at most 3, or when the automaton is not bireversible, the generated group cannot be Burnside infinite. In this paper, we extend these results to automata...
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متن کاملan automaton group: a computational case study
we introduce a two generated weakly branch contracting automaton group $g$ which is generated by a two state automaton on a three letter alphabet. using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. furthermore some algebraic properties of $g$ are detected .
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ژورنال
عنوان ژورنال: International Journal of Foundations of Computer Science
سال: 2018
ISSN: 0129-0541,1793-6373
DOI: 10.1142/s0129054118400087