scholarly journals On codes in the projective linear group PGL(2,q)

2021 ◽  
Vol 75 ◽  
pp. 101812
Author(s):  
Tao Feng ◽  
Weicong Li ◽  
Jingkun Zhou
Keyword(s):  
Linear Group ◽  
Projective Linear Group

Flag-Transitive 3- (v, k,3) Designs and PSL(2,q) Groups

2021 ◽  
Vol 28 (01) ◽  
pp. 33-38
Author(s):  
Shaojun Dai ◽  
Shangzhao Li
Keyword(s):  
Linear Group ◽  
Automorphism Groups ◽  
Two Dimensional ◽  
Text Design ◽  
Projective Linear Group

This article is a contribution to the study of the automorphism groups of 3-[Formula: see text] designs. Let [Formula: see text] be a non-trivial 3-[Formula: see text] design. If a two-dimensional projective linear group [Formula: see text] acts flag-transitively on [Formula: see text], then [Formula: see text] is a 3-[Formula: see text] or 3-[Formula: see text] design.

scholarly journals Automorphisms of Drinfeld half-spaces over a finite field

2013 ◽  
Vol 149 (7) ◽  
pp. 1211-1224 ◽  
Author(s):  
Bertrand Rémy ◽  
Amaury Thuillier ◽  
Annette Werner
Keyword(s):  
Automorphism Group ◽  
Finite Field ◽  
Vector Space ◽  
Half Space ◽  
Linear Group ◽  
Analytic Geometry ◽  
Base Field ◽  
Projective Linear Group

AbstractWe show that the automorphism group of Drinfeld’s half-space over a finite field is the projective linear group of the underlying vector space. The proof of this result uses analytic geometry in the sense of Berkovich over the finite field equipped with the trivial valuation. We also take into account extensions of the base field.

scholarly journals On a rationality problem for fields of cross-ratios II

2020 ◽  
pp. 1-11
Author(s):  
Tran-Trung Nghiem ◽  
Zinovy Reichstein
Keyword(s):  
Symmetric Group ◽  
Linear Group ◽  
Fixed Field ◽  
Independent Variables ◽  
Odd Order ◽  
Projective Linear Group ◽  
Rationality Problem

Abstract Let k be a field, $x_1, \dots , x_n$ be independent variables and let $L_n = k(x_1, \dots , x_n)$ . The symmetric group $\operatorname {\Sigma }_n$ acts on $L_n$ by permuting the variables, and the projective linear group $\operatorname {PGL}_2$ acts by $$ \begin{align*} \begin{pmatrix} a & b \\ c & d \end{pmatrix}\, \colon x_i \longmapsto \frac{a x_i + b}{c x_i + d} \end{align*} $$ for each $i = 1, \dots , n$ . The fixed field $L_n^{\operatorname {PGL}_2}$ is called “the field of cross-ratios”. Given a subgroup $S \subset \operatorname {\Sigma }_n$ , H. Tsunogai asked whether $L_n^S$ rational over $K_n^S$ . When $n \geqslant 5,$ the second author has shown that $L_n^S$ is rational over $K_n^S$ if and only if S has an orbit of odd order in $\{ 1, \dots , n \}$ . In this paper, we answer Tsunogai’s question for $n \leqslant 4$ .

scholarly journals The invariants of projective linear group actions

1989 ◽  
Vol 39 (1) ◽  
pp. 107-117 ◽  
Author(s):  
Huah Chu ◽  
Ming-Chang Kang ◽  
Eng-Tjioe Tan
Keyword(s):  
Rational Function ◽  
Linear Group ◽  
Function Field ◽  
Group Actions ◽  
Direct Computation ◽  
Rational Function Field ◽  
Projective Linear Group

Let Fq be the field with q elements and let G = PGLn(Fq) or PSLn(Fq) act on Fq(x1,…,xn−1), the rational function field of n − 1 variables. Then Fq(x1,…,xn−1)G is purely transcendental over Fq. In fact, a set of n − 1 generators of Fq(x1,…xn−1)G, over Fq is exhibited. The case n = 2 is treated by direct computation.

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