On the essential dimension of a finite group

Author: negs

August undefined, 2024

Web3 de abr. de 2013 · In the paper we survey research on the essential dimension. The highlights of the survey are the computations of the essential dimensions of finite … Web2 de fev. de 2024 · Download a PDF of the paper titled On the minimal dimension of a faithful linear representation of a finite group, by Alexander Moret\'o

Essential dimension: A survey Request PDF - ResearchGate

Web15 de dez. de 2024 · Thirdly we take locally finite presentation schemes, but this does not cause problems since the essential dimension of an algebraic affine group scheme is finite. If S is the spectrum of a field then by [2, Lemma 6.11 and Remark 6.12] the classical definition using compressions [2, Definition 6.8] of essential dimension is equivalent to … Web10 de out. de 2024 · I am chemist and ask for apologies for all my mathematical inabilities when asking this question in advance, but after quite a bit of searching I found that this problem could be "open" or at least hard enough to find addressed in the literature and also advanced enough that it's possibly suitable to be asked here. lithium cleaning

On the Essential Dimension of a Finite Group - School of …

Webon the essential dimension of alternating groups. Finally, in Section 7 we relate the essential dimension of a nite group Gto \versal" polynomials. This notion is related to … Web7 de jan. de 2011 · We show that Y. Prokhorov's "Simple Finite Subgroups of the Cremona Group of Rank 3" implies that, over any field of characteristic 0, the essential dimensions of the alternating group, A(7), and ... WebESSENTIAL DIMENSION OF FINITE p-GROUPS NIKITA A. KARPENKO AND ALEXANDER S. MERKURJEV Abstract. We prove that the essential dimension and p-dimension of a p-group G over a ﬁeld F containing a primitive p-th root of unity is equal to the least dimension of a faithful representation of G over F. impulse buying in a sentence

Quasi-Simple Finite Groups of Essential Dimension 3

Energies Free Full-Text MHD R&D Activities for Liquid …

Web6 de set. de 2024 · In this paper, we compute the essential p-dimension of the finite simple groups of classical Lie type at the defining prime, specifically the simple groups arising … impulse buying behaviour research papersWeb5 de fev. de 2024 · The notion of essential dimension of a finite group over a field k was introduced by Buhler and Reichstein [].It was later extended to various contexts. First Reichstein generalized it to linear algebraic groups [] in characteristic zero; afterwards Merkurjev gave a general definition for functors from the category of extension fields of … impulse buying behavior theory

"Web7 de jan. de 2011 · We show that Y. Prokhorov's "Simple Finite Subgroups of the Cremona Group of Rank 3" implies that, over any field of characteristic 0, the essential … " - On the essential dimension of a finite group

On the essential dimension of a finite group

Essential dimension of group schemes over a local scheme

WebEssential Dimension of Finite Groups by Wanshun Wong Doctor of Philosophy in Mathematics University of California, Los Angeles, 2012 Professor Alexander Merkurjev, Chair In this thesis we study the essential dimension of the rst Galois cohomology functors of nite groups. Following the result by N. A. Karpenko and A. S. Merkurjev about the … Web22 de jan. de 2010 · We discuss essential dimension of group schemes, with particular attention to infinitesimal group schemes. We prove that the essential dimension of a group scheme of finite type over a field k is at least equal to the difference between the dimension of its Lie algebra and its dimension. Furthermore, we show that the …

Did you know?

Web1 de jun. de 2013 · We compare the notions of essential dimension and stable cohomological dimension of a finite group G, prove that the latter is bounded by the length of any normal series with cyclic quotients for ... Web2 de fev. de 2024 · If a finite linear group G of dimension d is not completely reducible, then its characteristic is a prime, p say, and the factor group of G modulo the largest normal p-subgroup O p(G) may be ...

Web31 de mar. de 1997 · Abstract: We introduce and study the notion of essential dimension for linear algebraic groups defined over an algebraically closed fields of characteristic zero. … WebESSENTIAL DIMENSION OF FINITE p-GROUPS 3 If G is a ﬂnite group, we view G as a constant group over a ﬂeld F.Every G-torsor over SpecL has the form SpecK where K …

Web20 de nov. de 2024 · Essential dimension of finite p-groups. Inventiones mathematicae, Vol. 172, Issue. 3, p. 491. CrossRef; Google Scholar; Meyer, Aurel and Reichstein, Zinovy 2009. The essential dimension of the normalizer of a maximal torus in … WebESSENTIAL DIMENSION OF FINITE p-GROUPS 3 If G is a ﬂnite group, we view G as a constant group over a ﬂeld F.Every G-torsor over SpecL has the form SpecK where K is a Galois G-algebra over L.Therefore, ed(G) is the essential dimension of the functor taking a ﬂeld Lto the set of isomorphism classes of Galois G-algebras over L. Example 1.3.1. Let …

Weboverview of the theory of essential dimension, we refer the reader to the surveys [Rei10] and [Me13]. The case where G is a ﬁnite group (viewed as a constant group over F) …

WebThe concepts essential and finite dimension played an important role in the development of the dimension theory of modules over rings. Finite dimension, essential, strictly … impulse buying house gurgaonWeb1 de jan. de 2013 · The computation of the essential dimension is a challenging problem of algebra and algebraic geometry. The finite groups of essential dimension ≤ 2 have … impulse buying definition financeWebESSENTIAL Group, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, ... are not directly amenable to analysis by general-purpose CFD codes based on finite-volume or finite-element discretization on ... (three-dimensional, albeit anisotropic) turbulence can occur in typical blanket conditions only if poorly electrically ... impulse buying in indiaWebIn this thesis we study the essential dimension of the first Galois cohomology functors of finite groups. Following the result by N. A. Karpenko and A. S. Merkurjev about the essential dimension of finite p-groups over a field containing a primitive p-th root of unity, we compute the essential dimension of finite cyclic groups and finite abelian groups … lithium clientWebapproach to modules and linear algebra, a fresh take on Gröbner theory, and a group theoretic treatment of Rejewski's deciphering of the Enigma machine. It includes a detailed treatment of the basics on finite groups, including Sylow theory and the structure of finite abelian groups. Galois theory impulse buying journal model pdfWebJournal of Fluids and Structures 19 de julho de 2024. This paper examines an active mechanism of wake control for a turbulent flow regime of Reynolds number 1000 through finite volume, three-dimensional DES simulations. Eight peripheral rods equally spaced about a central body are forced to spin around their axes in two arrangements: case 0 ... lithium client educationWeb22 de nov. de 2006 · We study the essential dimension of a finite group G over a field K. A generalization of the central extension theorem of Buhler and Reichstein (Compositio Math. 106 (1997) 159-179, Theorem 5.3) is obtained. We also get lower bounds of essential dimension of symmetric groups and alternating groups over field of any characteristic. impulse buying journal