Upper Bounds on |L(1, χ)| and Applications

1998 ◽  
Vol 50 (4) ◽  
pp. 794-815 ◽  
Author(s):  
Stéphane Louboutin
Keyword(s):  
Finite Field ◽  
Galois Group ◽  
Linear Group ◽  
Class Number ◽  
Upper Bounds ◽  
Special Linear Group ◽  
Class Numbers ◽  
Special Linear ◽  
Abelian Extensions

AbstractWe give upper bounds on the modulus of the values at s = 1 of Artin L-functions of abelian extensions unramified at all the infinite places.We also explain how we can compute better upper bounds and explain how useful such computed bounds are when dealing with class number problems for CM-fields. For example, we will reduce the determination of all the non-abelian normal CM-fields of degree 24 with Galois group SL2(F3) (the special linear group over the finite field with three elements) which have class number one to the computation of the class numbers of 23 such CM-fields.

scholarly journals Principal indecomposable modules for some three-dimensional special linear groups

1980 ◽  
Vol 22 (3) ◽  
pp. 439-455 ◽  
Author(s):  
James Archer
Keyword(s):  
Finite Field ◽  
Linear Group ◽  
Three Dimensional ◽  
Special Linear Group ◽  
Linear Groups ◽  
Indecomposable Modules ◽  
Special Linear ◽  
Special Linear Groups ◽  
Irreducible Modules ◽  
Characteristic 2

Let k be a finite field of characteristic 2, and let G be the three dimensional special linear group over k. The principal indecomposable modules of G over k are constructed from tensor products of the irreducible modules, and formulae for their dimensions are given.

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.

scholarly journals Integral cohomology and Chern classes of the special linear group over the ring of integers

2001 ◽  
Vol 131 (3) ◽  
pp. 445-457
Author(s):  
DOMINIQUE ARLETTAZ ◽  
CHRISTIAN AUSONI ◽  
MAMORU MIMURA ◽  
NOBUAKI YAGITA
Keyword(s):  
Linear Group ◽  
Upper Bound ◽  
Special Linear Group ◽  
Discrete Groups ◽  
Chern Classes ◽  
Additive Structure ◽  
Special Linear ◽  
Ring Of Integers ◽  
Integral Cohomology ◽  
Complete Calculation

This paper is devoted to the complete calculation of the additive structure of the 2-torsion of the integral cohomology of the infinite special linear group SL(ℤ) over the ring of integers ℤ. This enables us to determine the best upper bound for the order of the Chern classes of all integral and rational representations of discrete groups.

scholarly journals The third homology of the special linear group of a field

2009 ◽  
Vol 213 (9) ◽  
pp. 1665-1680 ◽  
Author(s):  
Kevin Hutchinson ◽  
Liqun Tao
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Special Linear ◽  
The Third

On the existence of Engel pairs in certain linear groups

2016 ◽  
Vol 15 (04) ◽  
pp. 1650062
Author(s):  
S. G. Quek ◽  
K. B. Wong ◽  
P. C. Wong
Keyword(s):  
Linear Group ◽  
Field Extension ◽  
Special Linear Group ◽  
Linear Groups ◽  
Special Linear

Let [Formula: see text] be a group and [Formula: see text]. The 2-tuple [Formula: see text] is said to be an [Formula: see text]-Engel pair, [Formula: see text], if [Formula: see text], [Formula: see text] and [Formula: see text]. Let SL[Formula: see text] be the special linear group of degree [Formula: see text] over the field [Formula: see text]. In this paper, we show that given any field [Formula: see text], there is a field extension [Formula: see text] of [Formula: see text] with [Formula: see text] such that SL[Formula: see text] has an [Formula: see text]-Engel pair for some integer [Formula: see text]. We will also show that SL[Formula: see text] has a [Formula: see text]-Engel pair if [Formula: see text] is a field of characteristic [Formula: see text].

scholarly journals The special linear group for nonassociative rings

2020 ◽  
Vol 23 (2) ◽  
pp. 327-335
Author(s):  
Harry Petyt
Keyword(s):  
Linear Group ◽  
Special Linear Group ◽  
Large Classes ◽  
Special Linear ◽  
Lie Ring ◽  
Definition Of ◽  
Associative Rings

AbstractWe extend to arbitrary rings a definition of the octonion special linear group due to Baez. At the infinitesimal level, we get a Lie ring, which we describe over some large classes of rings, including all associative rings and all algebras over a field. As a corollary, we compute all the groups Baez defined.

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