NSE characterization of projective special linear group $L_5(2)$

2014 ◽  
Vol 132 ◽  
pp. 123-132 ◽  
Author(s):  
Shitian Liu
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Projective Special Linear Group ◽  
Special Linear

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.

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.

scholarly journals On Invariant Operations on a Manifold with a Linear Connection and an Orientation

Mathematics ◽  
2021 ◽  
Vol 9 (20) ◽  
pp. 2577
Author(s):  
Adrián Gordillo-Merino ◽  
Raúl Martínez-Bohórquez ◽  
José Navarro-Garmendia
Keyword(s):  
Linear Group ◽  
Linear Connection ◽  
Special Linear Group ◽  
Bianchi Identities ◽  
Special Linear ◽  
Linear Representations ◽  
Natural Operators

We prove a theorem that describes all possible tensor-valued natural operations in the presence of a linear connection and an orientation in terms of certain linear representations of the special linear group. As an application of this result, we prove a characterization of the torsion and curvature operators as the only natural operators that satisfy the Bianchi identities.

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.

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.

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