Generators of Subgroups of Finite Index in GL m (ℤG)

1997 ◽  
pp. 211-219
Author(s):  
Gregory T. Lee ◽  
Sudarshan K. Sehgal
Keyword(s):  
Finite Index

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.

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.

scholarly journals Subgroups of finite index in an additive group of a ring

2001 ◽  
Vol 27 (2) ◽  
pp. 83-89
Author(s):  
Doostali Mojdeh ◽  
S. Hassan Hashemi
Keyword(s):  
Finite Index ◽  
Additive Group ◽  
Infinite Field ◽  
Division Rings ◽  
Invertible Elements

IfKis an infinite field andG⫅Kis a subgroup of finite index in an additive group, thenK∗=G∗G∗−1whereG∗denotes the set of all invertible elements inGandG∗−1denotes all inverses of elements ofG∗. Similar results hold for various fields, division rings and rings.

Subgroups of Finite Index in Free Groups

1949 ◽  
Vol 1 (2) ◽  
pp. 187-190 ◽  
Author(s):  
Marshall Hall
Keyword(s):  
Free Group ◽  
Finite Index ◽  
Free Groups ◽  
Recursion Formula ◽  
Independent Interest ◽  
Finiteness Conditions ◽  
Total Length ◽  
Free Generators

This paper has as its chief aim the establishment of two formulae associated with subgroups of finite index in free groups. The first of these (Theorem 3.1) gives an expression for the total length of the free generators of a subgroup U of the free group Fr with r generators. The second (Theorem 5.2) gives a recursion formula for calculating the number of distinct subgroups of index n in Fr.Of some independent interest are two theorems used which do not involve any finiteness conditions. These are concerned with ways of determining a subgroup U of F.

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