scholarly journals Finite index theorems for iterated Galois groups of unicritical polynomials

2020 ◽  
Vol 374 (1) ◽  
pp. 733-752 ◽  
Author(s):  
Andrew Bridy ◽  
John R. Doyle ◽  
Dragos Ghioca ◽  
Liang-Chung Hsia ◽  
Thomas J. Tucker
Keyword(s):  
Finite Index ◽  
Galois Groups ◽  
Index Theorems ◽  
Unicritical Polynomials

scholarly journals Finite index theorems for iterated Galois groups of cubic polynomials

2018 ◽  
Vol 373 (1-2) ◽  
pp. 37-72 ◽  
Author(s):  
Andrew Bridy ◽  
Thomas J. Tucker
Keyword(s):  
Finite Index ◽  
Galois Groups ◽  
Index Theorems ◽  
Cubic Polynomials

scholarly journals A question for iterated Galois groups in arithmetic dynamics

2020 ◽  
pp. 1-17
Author(s):  
Andrew Bridy ◽  
John R. Doyle ◽  
Dragos Ghioca ◽  
Liang-Chung Hsia ◽  
Thomas J. Tucker
Keyword(s):  
Dynamical System ◽  
Galois Groups ◽  
General Question ◽  
Arithmetic Dynamics ◽  
Polynomial Maps ◽  
Special Cases ◽  
Unicritical Polynomials

Abstract We formulate a general question regarding the size of the iterated Galois groups associated with an algebraic dynamical system and then we discuss some special cases of our question. Our main result answers this question for certain split polynomial maps whose coordinates are unicritical polynomials.

scholarly journals Galois groups of iterates of some unicritical polynomials

2017 ◽  
Vol 181 (1) ◽  
pp. 57-73 ◽  
Author(s):  
Michael R. Bush ◽  
Wade Hindes ◽  
Nicole R. Looper
Keyword(s):  
Galois Groups ◽  
Unicritical Polynomials

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.

Free pro- $p$ product decompositions of Galois groups

1997 ◽  
Vol 225 (2) ◽  
pp. 245-261 ◽  
Author(s):  
Ido Efrat
Keyword(s):  
Galois Groups

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.

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