On Bounded Semilinear Languages, Counter Machines, and Finite-Index ET0L

2016 ◽  
pp. 138-149 ◽  
Author(s):  
Oscar H. Ibarra ◽  
Ian McQuillan
Keyword(s):  
Finite Index ◽  
Counter Machines

Automorphisms of finite order of nilpotent groups II

2014 ◽  
Vol 51 (4) ◽  
pp. 547-555 ◽  
Author(s):  
B. Wehrfritz
Keyword(s):  
Nilpotent Group ◽  
Finite Order ◽  
Finite Index ◽  
Nilpotent Groups ◽  
Finitely Generated

Let G be a nilpotent group with finite abelian ranks (e.g. let G be a finitely generated nilpotent group) and suppose φ is an automorphism of G of finite order m. If γ and ψ denote the associated maps of G given by \documentclass{aastex} \usepackage{amsbsy} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{bm} \usepackage{mathrsfs} \usepackage{pifont} \usepackage{stmaryrd} \usepackage{textcomp} \usepackage{upgreek} \usepackage{portland,xspace} \usepackage{amsmath,amsxtra} \usepackage{bbm} \pagestyle{empty} \DeclareMathSizes{10}{9}{7}{6} \begin{document} $$\gamma :g \mapsto g^{ - 1} \cdot g\phi and \psi :g \mapsto g \cdot g\phi \cdot g\phi ^2 \cdots \cdot \cdot g\phi ^{m - 1} for g \in G,$$ \end{document} then Gγ · kerγ and Gψ · ker ψ are both very large in that they contain subgroups of finite index in G.

scholarly journals Simple counter machines and number-theoretic problems

1979 ◽  
Vol 19 (2) ◽  
pp. 145-162 ◽  
Author(s):  
Eitan M. Gurari ◽  
Oscar H. Ibarra
Keyword(s):  
Counter Machines

On metalinear ETOL systems

1980 ◽  
Vol 3 (1) ◽  
pp. 15-36
Author(s):  
Grzegorz Rozenberg ◽  
Dirk Vermeir
Keyword(s):  
Finite Index ◽  
Closure Properties ◽  
Pumping Lemma ◽  
L Systems ◽  
Structural Characterizations

The concept of metalinearity in ETOL systems is investigated. Some structural characterizations, a pumping lemma and the closure properties of the resulting class of languages are established. Finally, some applications in the theory of L systems of finite index are provided.

On locally graded barely transitive groups

2013 ◽  
Vol 11 (7) ◽  
Author(s):  
Cansu Betin ◽  
Mahmut Kuzucuoğlu
Keyword(s):  
Finite Index ◽  
Cyclic Subgroup ◽  
Transitive Group ◽  
Transitive Groups ◽  
Point Stabilizer

AbstractWe show that a barely transitive group is totally imprimitive if and only if it is locally graded. Moreover, we obtain the description of a barely transitive group G for the case G has a cyclic subgroup 〈x〉 which intersects non-trivially with all subgroups and for the case a point stabilizer H of G has a subgroup H 1 of finite index in H satisfying the identity χ(H 1) = 1, where χ is a multi-linear commutator of weight w.

scholarly journals Multidimensional Multiplicative Combinatorial Properties of Dynamical Syndetic Sets

2021 ◽  
Author(s):  
Jiahao Qiu ◽  
Jianjie Zhao
Keyword(s):  
Normal Subgroup ◽  
Finite Index ◽  
Minimal System ◽  
Combinatorial Properties ◽  
Return Times ◽  
Residual Set ◽  
Closed Sets ◽  
Open Set ◽  
Geometric Progressions ◽  
Set Of Points

AbstractIn this paper, it is shown that for a minimal system (X, G), if H is a normal subgroup of G with finite index n, then X can be decomposed into n components of closed sets such that each component is minimal under H-action. Meanwhile, we prove that for a residual set of points in a minimal system with finitely many commuting homeomorphisms, the set of return times to any non-empty open set contains arbitrarily long geometric progressions in multidimension, extending a previous result by Glasscock, Koutsogiannis and Richter.

Representations of regular rings o f finite index-II

1993 ◽  
Vol 21 (11) ◽  
pp. 4173-4177 ◽  
Author(s):  
Andrew B. Carson
Keyword(s):  
Finite Index ◽  
Regular Rings

Groups with every subgroup ascendant-by-finite

2013 ◽  
Vol 11 (12) ◽  
Author(s):  
Sergio Camp-Mora
Keyword(s):  
Finite Group ◽  
Finite Index ◽  
Locally Finite Group ◽  
Locally Finite ◽  
Locally Nilpotent

AbstractA subgroup H of a group G is called ascendant-by-finite in G if there exists a subgroup K of H such that K is ascendant in G and the index of K in H is finite. It is proved that a locally finite group with every subgroup ascendant-by-finite is locally nilpotent-by-finite. As a consequence, it is shown that the Gruenberg radical has finite index in the whole group.

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