Lamplighter groups, bireversible automata, and rational series over finite rings
نویسندگان
چکیده
منابع مشابه
Extended finite automata over groups
Some results from Dassow and Mitrana (Internat. J. Comput. Algebra (2000)), Griebach (Theoret. Comput. Sci. 7 (1978) 311) and Ibarra et al. (Theoret. Comput. Sci. 2 (1976) 271) are generalized for finite autómata over arbitrary groups. The closure properties of these autómata are poorer and the accepting power is smaller when abelian groups are considered. We prove that the addition of any abel...
متن کاملCross-wired lamplighter groups and linearity of automata groups
We consider the two generalizations of lamplighter groups: automata groups generated by Cayley machines and cross-wired lamplighter groups. For a finite step two nilpotent group with central squares, we study its associated Cayley machine and give a presentation of the corresponding automata group. We show the automata group is a crosswired lamplighter group and does not embed in the wreath pro...
متن کاملRepresentations of Reductive Groups over Finite Rings
In this paper we construct a family of irreducible representations of a Chevalley group over a finite ring R of truncated power series over a field Fq . This is done by a cohomological method extending that of Deligne and the author in the case R = Fq .
متن کاملOn 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.
متن کاملRATIONAL CHARACTER TABLE OF SOME FINITE GROUPS
The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational character tables are also considered into account.The aim of this paper is to compute the rational character tables of the dicyclic group $T_{4n}$, the groups of order $pq$ and $pqr$. Some general properties of rational charact...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Groups, Geometry, and Dynamics
سال: 2020
ISSN: 1661-7207
DOI: 10.4171/ggd/555