scholarly journals Cyclotomic equations and square properties in rings

1986 ◽  
Vol 9 (1) ◽  
pp. 89-95
Author(s):  
Benjamin Fine
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Sum Of Squares ◽  
Polynomial Rings ◽  
Projective Special Linear Group ◽  
Infinite Class ◽  
Related Property ◽  
Special Linear

IfRis a ring, the structure of the projective special linear groupPSL2(R)is used to investigate the existence of sum of square properties holding inR. Rings which satisfy Fermat's two-square theorem are called sum of squares rings and have been studied previously. The present study considers a related property called square property one. It is shown that this holds in an infinite class of rings which includes the integers, polynomial rings over many fields andZpnwherePis a prime such that−3is not a squaremodp. Finally, it is shown that the class of sum of squares rings and the class satisfying square property one are non-coincidental.

scholarly journals De non ordinaria recognitione PSL2

2008 ◽  
Vol 7 (4) ◽  
pp. 723-734
Author(s):  
Adrien Deloro
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Morley Rank ◽  
Projective Special Linear Group ◽  
Special Linear ◽  
Dimension 2

AbstractWe establish an identification result of the projective special linear group of dimension 2 among a certain class of groups the Morley rank of which is finite.

Centralizers in a group whose central factor is simple

2018 ◽  
Vol 17 (08) ◽  
pp. 1850149
Author(s):  
Seyyed Majid Jafarian Amiri ◽  
Hojjat Rostami
Keyword(s):  
Finite Group ◽  
Linear Group ◽  
Finite Groups ◽  
Special Linear Group ◽  
Projective Special Linear Group ◽  
Special Linear ◽  
Central Factor ◽  
Suzuki Group ◽  
A Finite Group ◽  
Appl Math

In this paper, we find the number of the element centralizers of a finite group [Formula: see text] such that the central factor of [Formula: see text] is the projective special linear group of degree 2 or the Suzuki group. Our results generalize some main results of [Ashrafi and Taeri, On finite groups with a certain number of centralizers, J. Appl. Math. Comput. 17 (2005) 217–227; Schmidt, Zentralisatorverbände endlicher Gruppen, Rend. Sem. Mat. Univ. Padova 44 (1970) 97–131; Zarrin, On element centralizers in finite groups, Arch. Math. 93 (2009) 497–503]. Also, we give an application of these results.

scholarly journals A further characterization of a projective special linear group

1977 ◽  
Vol 24 (1) ◽  
pp. 112-116 ◽  
Author(s):  
Saad Adnan
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Projective Special Linear Group ◽  
Special Linear

AbstractIn this paper we present a characterization of PSL(2,7) by a condition different from that given in our previous paper.

Erdös-Ko-Rado theorem in some linear groups and some projective special linear group

2014 ◽  
Vol 51 (1) ◽  
pp. 83-91
Author(s):  
Milad Ahanjideh ◽  
Neda Ahanjideh
Keyword(s):  
Finite Field ◽  
Vector Space ◽  
Prime Number ◽  
Linear Group ◽  
Projective Line ◽  
Special Linear Group ◽  
Linear Groups ◽  
Projective Special Linear Group ◽  
Special Linear ◽  
Derangement Graph

Let V be the 2-dimensional column vector space over a finite field \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} $$\mathbb{F}_q$$ \end{document} (where q is necessarily a power of a prime number) and let ℙq be the projective line over \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} $$\mathbb{F}_q$$ \end{document}. In this paper, it is shown that GL2(q), for q ≠ 3, and SL2(q) acting on V − {0} have the strict EKR property and GL2(3) has the EKR property, but it does not have the strict EKR property. Also, we show that GLn(q) acting on \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} $$\left( {\mathbb{F}_q } \right)^n - \left\{ 0 \right\}$$ \end{document} has the EKR property and the derangement graph of PSL2(q) acting on ℙq, where q ≡ −1 (mod 4), has a clique of size q + 1.

Products of Elations and Harmonic Homologies

1985 ◽  
Vol 28 (4) ◽  
pp. 397-400 ◽  
Author(s):  
Erich W. Ellers
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Projective Special Linear Group ◽  
Special Linear ◽  
Unimodular Group ◽  
Number Of Factors ◽  
Special Cases

AbstractThe projective special linear group PSL(V) is generated by dations. Among all factorizations of p ∈ PSL(V) into dations there will be one (or more) with the least number of factors. We determine this number, i.e. we solve the length problem for the projective special linear group. We solve a similar problem for the projective unimodular group which is generated by harmonic homologies. The projective special linear group and the projective unimodular group are the most important special cases of projective hyperreflection groups. We also solve the length problem for the general case.

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