A Fractal Non-Contracting Class of Automata Groups

a fractal non-contracting class of automata groups

commuting and non -commuting graphs of finit groups

فرض کنیمg یک گروه غیر آبلی متناهی باشد . گراف جابجایی g که با نماد نمایش داده می شود ،گرافی است ساده با مجموعه رئوس که در آن دو راس با یک یال به هم وصل می شوند اگر و تنها اگر . مکمل گراف جابجایی g راگراف نا جابجایی g می نامیم.و با نماد نشان می دهیم. گرافهای جابجایی و ناجابجایی یک گروه متناهی ،اولین بار توسطاردوش1 مطرح گردید ،ولی در سالهای اخیر به طور مفصل در مورد بحث و بررسی قرار گرفتند . در ،م...

On a Class of Automata Groups Generalizing Lamplighter Groups

We study automata groups generated by reset automata. Every lamplighter group Z/nZ wr Z can be generated by such an automaton, and in general these automata groups are similar in nature to lamplighters: they are amenable locally-finite-by-cyclic groups; under mild decidable conditions, the semigroups generated by such automata are free. Parabolic subgroups and fractal properties are considered.

The fractal structure of cellular automata on abelian groups

It is a well-known fact that the spacetime diagrams of some cellular automata have a fractal structure: for instance Pascal’s triangle modulo 2 generates a Sierpinski triangle. Explaining the fractal structure of the spacetime diagrams of cellular automata is a much explored topic, but virtually all of the results revolve around a special class of automata, whose main features include irreversi...

Groups with one conjugacy class of non-normal subgroups‎ - ‎a short proof

For a finite group $G$ let $nu(G)$ denote the number of conjugacy classes of non-normal subgroups of $G$. We give a short proof of a theorem of Brandl, which classifies finite groups with $nu(G)=1$.

Non-Uniform Automata Over Groups

A new model, non-uniform deterministic finite automata (NUDFA’s) over general tinite monoids, has recently been developed as a strong link between the theory of finite automata and low-level parallel complexity. Achievements of this model include the proof that width 5 branching programs recognize exactly the languages in non-uniform NC’, NUDFA characterizations of several important subclasses ...