scholarly journals Testing polycyclicity of finitely generated rational matrix groups

2007 ◽  
Vol 76 (259) ◽  
pp. 1669-1683 ◽  
Author(s):  
Björn Assmann ◽  
Bettina Eick
Keyword(s):  
Rational Matrix ◽  
Finitely Generated ◽  
Matrix Groups

NILPOTENT AND LOCALLY FINITE MAXIMAL SUBGROUPS OF SKEW LINEAR GROUPS

2011 ◽  
Vol 10 (04) ◽  
pp. 615-622 ◽  
Author(s):  
M. RAMEZAN-NASSAB ◽  
D. KIANI
Keyword(s):  
Maximal Subgroup ◽  
Natural Number ◽  
Division Ring ◽  
Subnormal Subgroup ◽  
Maximal Subgroups ◽  
Linear Groups ◽  
Finitely Generated ◽  
Locally Finite ◽  
Matrix Groups ◽  
Nilpotent Maximal Subgroup

Let D be a division ring and N be a subnormal subgroup of D*. In this paper we prove that if M is a nilpotent maximal subgroup of N, then M′ is abelian. If, furthermore every element of M is algebraic over Z(D) and M′ ⊈ F* or M/Z(M) or M′ is finitely generated, then M is abelian. The second main result of this paper concerns the subgroups of matrix groups; assume D is a noncommutative division ring, n is a natural number, N is a subnormal subgroup of GLn(D), and M is a maximal subgroup of N. We show that if M is locally finite over Z(D)*, then M is either absolutely irreducible or abelian.

scholarly journals An embedding theorem for fields

1976 ◽  
Vol 14 (2) ◽  
pp. 193-198 ◽  
Author(s):  
J.W.S. Cassels
Keyword(s):  
Simple Proof ◽  
Embedding Theorem ◽  
Normal Subgroups ◽  
Finitely Generated ◽  
Matrix Groups ◽  
Recurrent Sequences ◽  
Finite Set ◽  
Torsion Free

It is shown that every finitely generated field K of characteristic 0 may be embedded in infinitely many p-adic fields in such a way that the images of any given finite set C of non-zero elements of K are p-adic units. The result is suggested by Lech's proof of his generalization of Mahler's theorem on recurrent sequences. It also provides a simple proof of Selberg's theorem about torsion-free normal subgroups of matrix groups.

scholarly journals On Deciding Finiteness for Matrix Groups over Fields of Positive Characteristic

2001 ◽  
Vol 4 ◽  
pp. 64-72 ◽  
Author(s):  
A. Detinko
Keyword(s):  
Finite Field ◽  
Positive Characteristic ◽  
Deterministic Algorithm ◽  
Transcendence Degree ◽  
Matrix Group ◽  
Finitely Generated ◽  
Matrix Groups ◽  
Field Of Positive Characteristic

AbstractThe author considers the development of algorithms for deciding whether a finitely generated matrix group over a field of positive characteristic is finite. A deterministic algorithm for deciding the finiteness is presented for the case of a field of transcendence degree one over a finite field.

scholarly journals Finite rational matrix groups

1995 ◽  
Vol 116 (556) ◽  
pp. 0-0 ◽  
Author(s):  
G. Nebe ◽  
W. Plesken
Keyword(s):  
Rational Matrix ◽  
Matrix Groups

scholarly journals Computing polycyclic presentations for polycyclic rational matrix groups

2005 ◽  
Vol 40 (6) ◽  
pp. 1269-1284 ◽  
Author(s):  
Björn Assmann ◽  
Bettina Eick
Keyword(s):  
Rational Matrix ◽  
Matrix Groups

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.

Collectives of Automata in Finitely Generated Groups

2020 ◽  
Vol 108 (5-6) ◽  
pp. 671-678
Author(s):  
D. V. Gusev ◽  
I. A. Ivanov-Pogodaev ◽  
A. Ya. Kanel-Belov
Keyword(s):  
Finitely Generated ◽  
Finitely Generated Groups
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