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
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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 ...
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The étale cohomology of the general linear group over a finite field and the Dickson algebra
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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Linearizing torsion classes in the Picard group of algebraic curves over finite fields
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.
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Khronos, 2016 This paper stresses a specific line of development of the notion of finite field, from Évariste Galois’s 1830 “Note sur la théorie des nombres,” and Camille Jordan’s 1870 Traité des substitutions et des équations algébriques, to Leonard Dickson’s 1901 ...
Frédéric BRECHENMACHER
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One algebra of double cosets for a general linear group over a finite field
Let $\mathbb {F}_q$ be finite field with $q$ elements. Let $α\leqslant n$ be positive integers. Consider the general linear group $\mathrm{GL}(α+n, \mathbb {F}_q) $ and its subgroup $H(n)$, which fixes the first $α$ basis elements in $\mathbb {F}_q^{α+n}$. Denote $\mathcal{A}_n$ by the convolution algebra of $H(n)$-biinvariant functions on $\mathrm{GL}(
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Let F be a non-archimedean local field of characteristic zero whose residue field has at least three elements. Let G be an almost simple linear algebraic group over F, with rank_F(G) >= 2. Let X be a simply connected symmetric space of infinite dimension and finite rank, with non-positive curvature operator.
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Accelerated Multisecret Sharing Scheme Using Fast Matrix Spectral Factorization. [PDF]
Entropy (Basel)Çalkavur S, Solé P, Ephremidze L.
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Noncyclic BCH and Srivastava codes over the subgroup of the groups of units of Galois rings [Formula: see text] for advanced error control. [PDF]
Sci RepSajjad M +4 more
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A Survey of Lattice-Based Physical-Layer Security for Wireless Systems with <i>p</i>-Modular Lattice Constructions. [PDF]
Entropy (Basel)Khodaiemehr H +5 more
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