scholarly journals Computing a Chief Series and the Soluble Radical of a Matrix Group Over a Finite Field

2008 ◽  
Vol 11 ◽  
pp. 223-251 ◽  
Author(s):  
Derek F. Holt ◽  
Mark J. Stather
Keyword(s):  
Finite Field ◽  
Matrix Group ◽  
Matrix Groups ◽  
Generating Set

AbstractWe describe an algorithm for computing a chief series, the soluble radical, and two other characteristic subgroups of a matrix group over a finite field, which is intended for matrix groups that are too large for the use of base and strong generating set methods. The algorithm has been implemented in Magma by the second author.

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.

Matrix Group Actions Transforming Patterns

2006 ◽  
Author(s):  
Ulf Grenander ◽  
Michael I. Miller
Keyword(s):  
Coordinate System ◽  
Spatial Patterns ◽  
Group Actions ◽  
Temporal Patterns ◽  
Matrix Group ◽  
Matrix Groups ◽  
Pattern Theory ◽  
Complex Patterns

Thus far Pattern theory has been combinatore constructing complex patterns by connecting simpler ones via graphs. Patterns typically occurring in nature may be extremely complex and exhibit invariances. For example, spatial patterns may live in a space where the choice of coordinate system is irrelevant; temporal patterns may exist independently of where time is counted from, and so on. For this matrix groups as transformations are introduced, these transformations often forming groups which act on the generators.

scholarly journals A recognition algorithm for non-generic classical groups over finite fields

1999 ◽  
Vol 67 (2) ◽  
pp. 223-253 ◽  
Author(s):  
Azice C. Niemeyer ◽  
Cheryl E. Praeger
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Special Linear Group ◽  
Theoretical Background ◽  
Recognition Algorithm ◽  
Large Field ◽  
Matrix Group ◽  
Classical Groups ◽  
Original Algorithm ◽  
The Matrix

AbstractIn a previous paper the authors described an algorithm to determine whether a group of matrices over a finite field, generated by a given set of matrices, contains one of the classical groups or the special linear group. The algorithm was designed to work for all sufficiently large field sizes and dimensions of the matrix group. However, it did not apply to certain small cases. Here we present an algorithm to handle the remaining cases. The theoretical background of the algorithm presented in this paper is a substantial extension of that needed for the original algorithm.

LINEAR GROUPS OF SMALL DEGREE OVER FINITE FIELDS

2005 ◽  
Vol 15 (03) ◽  
pp. 467-502 ◽  
Author(s):  
D. L. FLANNERY ◽  
E. A. O'BRIEN
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Small Degree ◽  
Linear Groups ◽  
Generating Set

For n = 2,3 and finite field 𝔼 of characteristic greater than n, we provide a complete and irredundant list of soluble irreducible subgroups of GL (n,𝔼). The insoluble irreducible subgroups of GL (2,𝔼) are similarly determined. Each group is given explicitly by a generating set of matrices. The lists are available electronically.

A THEOREM ON MATRIX GROUPS

2008 ◽  
Vol 18 (01) ◽  
pp. 165-180
Author(s):  
A. I. PAPISTAS
Keyword(s):  
Abelian Group ◽  
Finite Subset ◽  
Free Abelian Group ◽  
Principal Ideal Domain ◽  
Matrix Groups ◽  
Generating Set ◽  
Torsion Free Abelian Group ◽  
Group Of Units ◽  
Multiplicative Monoid ◽  
Torsion Free

Let K be a principal ideal domain, and An, with n ≥ 3, be a finitely generated torsion-free abelian group of rank n. Let Ω be a finite subset of KAn\{0} and U(KAn) the group of units of KAn. For a multiplicative monoid P generated by U(KAn) and Ω, we prove that any generating set for [Formula: see text] contains infinitely many elements not in [Formula: see text]. Furthermore, we present a way of constructing elements of [Formula: see text] not in [Formula: see text] for n ≥ 3. In the case where K is not a field the aforementioned results hold for n ≥ 2.

scholarly journals K-groups of rings and the homology of their elementary matrix groups

1985 ◽  
Vol 38 (2) ◽  
pp. 268-274
Author(s):  
Janet Aisbett
Keyword(s):  
Commutative Ring ◽  
Matrix Group ◽  
Elementary Matrix ◽  
Matrix Groups ◽  
Group Homology ◽  
Low Dimensional

AbstractLow dimensional algebraic K-groups of a commutative ring are described in terms of the homology of its elementary matrix group. This approach is prompted by recent successful computations of low-dimensional K-groups using group homology methods, and it builds on the identity K2(R)=H2(ER).

Acellular dermal matrix contributes to epithelialization in patients with chronic sinusitis

2019 ◽  
Vol 33 (8) ◽  
pp. 1053-1059
Author(s):  
Zhong Bing ◽  
Liu Feng ◽  
Chun-Shu Wu ◽  
Jin-Tao Du ◽  
Ya-Feng Liu ◽  
...  
Keyword(s):  
Chronic Sinusitis ◽  
Acellular Dermal Matrix ◽  
Gelatin Sponge ◽  
Matrix Group ◽  
Control Group ◽  
Nasal Surgery ◽  
Dermal Matrix ◽  
Mucosal Repair ◽  
Matrix Groups ◽  
Acellular Dermal

Background Nasal endoscopic surgery is widely used for nasal diseases, including sinusitis and tumors. However, scar hyperplasia, nasal irritation, scab, and nasal obstruction delay nasal mucosal recovery, with prolonged cleaning exacerbating the patient's financial burden. Here, we presented a novel approach for the treatment of nasal mucosal defects, termed acellular dermal matrix. Methods A total of 31 patients with bilateral chronic sinusitis (maxillary sinusitis and ethmoid sinusitis) underwent nasal surgery and nasal mucosal repair in September–October 2016. We divided the nasal cavities of each patient into control and acellular dermal matrix groups, randomly selected one side for nasal mucosal repair by surgery. A suitable acellular dermal matrix size was selected according to the defect in each patient. After pruning, the acellular dermal matrix was placed on the wound surface and filled with gelatin sponge. All patients were followed up for 14 weeks to compare nasal mucosal epithelialization between the control and acellular dermal matrix groups. Results：No obvious complications and adverse reactions were observed after nasal surgery. Lund-Kennedy scores in the acellular dermal matrix group were significantly decreased compared with the control group at 8 (0 (0, 1) vs. 2 (2, 4); P<0.05) weeks. Epithelialization time of eight weeks in the acellular dermal matrix groups was significantly decreased than the control group of 14 weeks. Conclusion Acellular dermal matrix provides a growth framework for the healthy mucosa on the wounded surface and reduces postoperative epithelialization time.

scholarly journals LSMR Iterative Method for General Coupled Matrix Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-12
Author(s):  
F. Toutounian ◽  
D. Khojasteh Salkuyeh ◽  
M. Mojarrab
Keyword(s):  
Iterative Method ◽  
Symmetric Matrix ◽  
Matrix Group ◽  
Frobenius Norm ◽  
Matrix Equations ◽  
Approximation Solution ◽  
Matrix Groups ◽  
Special Cases ◽  
Least Frobenius Norm Solution ◽  
General Coupled Matrix Equations

By extending the idea of LSMR method, we present an iterative method to solve the general coupled matrix equations∑k=1qAikXkBik=Ci,i=1,2,…,p, (including the generalized (coupled) Lyapunov and Sylvester matrix equations as special cases) over some constrained matrix groups(X1,X2,…,Xq), such as symmetric, generalized bisymmetric, and(R,S)-symmetric matrix groups. By this iterative method, for any initial matrix group(X1(0),X2(0),…,Xq(0)), a solution group(X1*,X2*,…,Xq*)can be obtained within finite iteration steps in absence of round-off errors, and the minimum Frobenius norm solution or the minimum Frobenius norm least-squares solution group can be derived when an appropriate initial iterative matrix group is chosen. In addition, the optimal approximation solution group to a given matrix group(X¯1,X¯2,…,X¯q)in the Frobenius norm can be obtained by finding the least Frobenius norm solution group of new general coupled matrix equations. Finally, numerical examples are given to illustrate the effectiveness of the presented method.

scholarly journals Best Approximations in Hardy Spaces on Infinite-Dimensional Unitary Matrix Groups

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Oleh Lopushansky
Keyword(s):  
Hardy Space ◽  
Hardy Spaces ◽  
Matrix Group ◽  
Unitary Matrix ◽  
Fock Spaces ◽  
Best Approximations ◽  
Matrix Groups ◽  
Infinite Dimensional ◽  
Type Interpolation ◽  
Complex Functions

We investigate the problem of best approximations in the Hardy space of complex functions, defined on the infinite-dimensional unitary matrix group. Applying an abstract Besov-type interpolation scale and the Bernstein-Jackson inequalities, a behavior of such approximations is described. An application to best approximations in symmetric Fock spaces is shown.

Unipotent normal subgroups of skew linear groups

1989 ◽  
Vol 105 (1) ◽  
pp. 37-51 ◽  
Author(s):  
B. A. F. Wehrfritz
Keyword(s):  
Normal Subgroup ◽  
Matrix Group ◽  
Linear Groups ◽  
Normal Subgroups ◽  
Matrix Groups ◽  
Division Rings ◽  
Additional Assumptions

A recurrent problem over many years in the study of linear groups has been the determination of the central height of a unipotent normal subgroup of some matrix group of specified type. In the theory of matrix groups over division rings, unipotent elements frequently present special difficulties and these have usually been by-passed by the addition of some suitable hypothesis. In this paper we make a start on the removal of these extraneous hypotheses. Our motivation for doing this now conies from [9], where by 3·7 of that paper the additional assumptions have finally reduced us to degree one, a situation where unipotent elements present few problems!

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