Titlebook: Cellular Automata and Groups; Tullio Ceccherini-Silberstein,Michel Coornaert Textbook 2023Latest edition The Editor(s) (if applicable) and

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Fundamentale Aspekte der Optionsbewertung,n is defined as being a map from the group into the alphabet. Thus, a configuration is a way of attaching an element of the alphabet to each element of the group. There is a natural action of the group on the set of configurations which is called the shift action (see Sect. 1.1).

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https://doi.org/10.1007/978-3-031-43328-3Cellular Automaton; Grigorchuk Group; Paradoxical Decomposition; Symbolic Dynamics; Gromov-Weiss Theorem

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978-3-031-43330-6The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl

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Optionsscheine als AnlagealternativeSurjunctive groups are defined in Sect. 3.1 as being the groups on which all injective cellular automata with finite alphabet are surjective. In Sect. 3.2 it is shown that every subgroup of a surjunctive group is a surjunctive group and that every locally surjunctive group is surjunctive.

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https://doi.org/10.1007/978-3-322-86019-4This chapter is devoted to the class of amenable groups. This is a class of groups which plays an important role in many areas of mathematics such as ergodic theory, harmonic analysis, representation theory, dynamical systems, geometric group theory, probability theory and statistics.

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