Results 1 to 10 of about 162,768 (165)
On Finite Subgroups in the General Linear Groups over an Algebraic Number Field
Journal of Physics: Conference Series, 2022 Abstract As is well-known, there are only finitely many isomorphic classes of finite subgroups in a given general linear group over the field of rational numbers. This result can be generalized to any algebraic number field. While the case of field of rational numbers is relatively well-studied, we still do not know much for general ...
Ying Li
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Linearizing torsion classes in the Picard group of algebraic curves over finite fields [PDF]
Journal of Algebra, 2009 We address the problem of computing in the group of $\ell^k$-torsion rational points of the jacobian variety of algebraic curves over finite fields, with a view toward computing modular representations.
Jean-Marc Couveignes
openaire +5 more sources
Definability of linear equation systems over groups and rings [PDF]
Logical Methods in Computer Science, 2013 Motivated by the quest for a logic for PTIME and recent insights that the descriptive complexity of problems from linear algebra is a crucial aspect of this problem, we study the solvability of linear equation systems over finite groups and rings from ...
Anuj Dawar +4 more
doaj +8 more sources
The étale cohomology of the general linear group over a finite field and the Dickson algebra [PDF]
Kyoto Journal of Mathematics, 2018 Let \(p\) and \(l\) be two different primes and \(X\) be a smooth algebraic variety over a finite field \(k= \mathbb F_p\). Let \({H^*}_{\mathrm{et}} (X, \mathbb Z/l)\) be the étale cohomology of \(X\) over \(k\). It is known that the cohomology of the classifying space (Milnor space) \(BG\) of any algebraic group \(G\) can be computed by smooth ...
Tezuka, Michishige, Yagita, Nobuaki
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Irreducible subgroups of simple algebraic groups - a survey [PDF]
Groups St Andrews 2017 in Birmingham, 2018 Let $G$ be a simple linear algebraic group over an algebraically closed field $K$ of characteristic $p \geqslant 0$, let $H$ be a proper closed subgroup of $G$ and let $V$ be a nontrivial finite dimensional irreducible rational $KG$-module. We say that $(
Burness +10 more
core +5 more sources
Hecke algebra isomorphisms and adelic points on algebraic groups [PDF]
Documenta Mathematica, 2015 Let $G$ denote a linear algebraic group over $\mathbf{Q}$ and $K$ and $L$ two number fields. Assume that there is a group isomorphism of points on $G$ over the finite adeles of $K$ and $L$, respectively.
Cornelissen, Gunther +1 more
core +3 more sources
Polynomial maps over finite fields and residual finiteness of mapping tori of group endomorphisms
, 2003 We prove that every mapping torus of any free group endomorphism is residually finite. We show how to use a not yet published result of E. Hrushovski to extend our result to arbitrary linear groups.
Alexander Borisov +14 more
core +2 more sources
Algebraic groups over finite fields: Connections between subgroups and isogenies [PDF]
Journal of group theroy, 2022 Let 𝐺 be a linear algebraic group defined over a finite field F q \mathbb{F}_{q} . We present several connections between the isogenies of 𝐺 and the finite groups of rational points ( G ( F q n ) ) n ≥ 1 (G(\mathbb{F}_{\smash{q^{n}}}))_{n\geq 1} .
Davide Sclosa
semanticscholar +1 more source
Multiband linear cellular automata and endomorphisms of algebraic vector groups [PDF]
arXiv.org, 2022 We propose a correspondence between certain multiband linear cellular automata - models of computation widely used in the description of physical phenomena - and endomorphisms of certain algebraic unipotent groups over finite fields.
J. Byszewski, G. Cornelissen
semanticscholar +1 more source
Boundedness for finite subgroups of linear algebraic groups [PDF]
, 2020 We show the boundedness of finite subgroups in any anisotropic reductive algebraic group over a perfect field that contains all roots of 1. Also, we provide explicit bounds for orders of finite subgroups of automorphism groups of Severi-Brauer varieties ...
C. Shramov, V. Vologodsky
semanticscholar +1 more source