منابع مشابه
Non-elementary amenable subgroups of automata groups
We consider groups of automorphisms of locally finite trees, and give conditions on its subgroups that imply that they are not elementary amenable. This covers all known examples of groups that are not elementary amenable and act on the trees: groups of intermediate growths and Basilica group, by giving a more straightforward proof. Moreover, we deduce that all finitely generated branch groups ...
متن کاملAmenable Groups
Throughout we let Γ be a discrete group. For f : Γ → C and each s ∈ Γ we define the left translation action by (s.f)(t) = f(s−1t). Definition 1.1. A group Γ is amenable is there exists a state μ on l∞(Γ) which is invariant under the left translation action: for all s ∈ Γ and f ∈ l∞(Γ), μ(s.f) = μ(f). Example 1.2. Finite groups are amenable: take the state which sends χ{s} to 1 |Γ| for each s ∈ ...
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The dynamics group of an asynchronous cellular automaton (ACA) relates properties of its long term dynamics to the structure of Coxeter groups. The key mathematical feature connecting these diverse fields is involutions. Group-theoretic results in the latter domain may lead to insight about the dynamics in the former, and vice-versa. In this article, we highlight some central themes and common ...
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Let V be a finite-dimensional vector space over a field K and let G be a sofic group. We show that every injective linear cellular automaton τ : V G → V G is surjective. As an application, we obtain a new proof of the stable finiteness of group rings of sofic groups, a result previously established by G. Elek and A. Szabó using different methods.
متن کاملExploring and Exploiting Quantum-Dot Cellular Automata
The Full Adders (FAs) constitute the essential elements of digital systems, in a sense that they affect the circuit parameters of such systems. With respect to the MOSFET restrictions, its replacement by new devices and technologies is inevitable. QCA is one of the accomplishments in nanotechnology nominated as the candidate for MOSFET replacement. In this article 4 new layouts are presente...
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ژورنال
عنوان ژورنال: Annales de l’institut Fourier
سال: 1999
ISSN: 0373-0956
DOI: 10.5802/aif.1686