On the essential dimension of a finite group

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August undefined, 2024

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. 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 …

(PDF) On the Essential Dimension of a Finite Group

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 ... Web1 de mai. de 2024 · Finite groups of essential dimension one. J. Algebra, 311 (1) (2007), pp. 31-37. MR2309876. Article. Download PDF View Record in Scopus Google Scholar. R. Lötscher, M. MacDonald, A. Meyer, Z. Reichstein. Essential p-dimension of algebraic groups whose connected component is a torus. dhc astaxanthin collagen gel

[math/0611673] Essential dimensions of finite groups

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 … 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 … Web4 de dez. de 2007 · On the essential dimension of a finite group - Volume 106 Issue 2. Skip to main content Accessibility help We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to … c# if statement order of evaluation

Application of Multihomogeneous Covariants to the Essential Dimension ...

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 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 … c if statements with charWeb24 de nov. de 2008 · We investigate essential dimension of finite groups over arbitrary fields and give a systematic treatment of multihomogenization, introduced by H.Kraft, G.Schwarz and the author. We generalize the central extension theorem of Buhler and Reichstein and use multihomogenization to substitute and generalize the stack-involved … dhc bass cabs

"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 … " - On the essential dimension of a finite group

On the essential dimension of a finite group

WebWe 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) …

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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 … Web22 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.

WebAuthor: Karl-Hermann Neeb Publisher: Springer Science & Business Media ISBN: 0817647414 Category : Mathematics Languages : en Pages : 492 Download Book. Book Description This collection of invited expository articles focuses on recent developments and trends in infinite-dimensional Lie theory, which has become one of the core areas of … Web1 de mar. de 2013 · We give an upper bound for the essential dimension of a smooth unipotent algebraic group over an arbitrary field. We also show that over a field k which is finitely generated over a perfect field, a smooth unipotent algebraic k -group is of essential dimension 0 if and only if it is k -split. Journal of Pure and Applied Algebra 217 (2013) …

WebThis generalizes a classical theorem of Felix Klein on quintic polynomials and is related to an algebraic form of Hilbert‘s 13th problem. Our approach to this question (and … WebOur approach to this question (and generalizations) is based on the idea of the “essential dimension ” of a finite group G: the smallest possible dimension of an algebraic G …

Web10 de abr. de 2024 · When functioning in normal situations, organizations adjust to complexity within a certain level of resilience, but information, resources and time are always finite, which affects such adjustments. Thus, when unexpected events occur—and healthcare is prone to unexpected events—the adjustments may not be enough to keep …

Web12 de set. de 2024 · A. Beauville, “Finite simple groups of small essential dimension,” in Trends in Contemporary Mathematics. Selected Talks Based on the Presentations at the INdAM Day, June 18, 2014, Springer, Cham (2014), pp. 221–228. c++ if statements with multiple conditionsWeb1 de mai. de 2024 · Let F be a field of characteristic p > 0 and G be a smooth finite algebraic group over F. Then ed F (G; p) = {1, if p divides G , and 0, otherwise. In … dhc at redbird squareWeb10 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. c if statement stringWebOur approach to this question (and generalizations) is basedon the idea of the ’essential dimension‘ of a finite group G:the smallest possible dimension of an algebraic G … c++ if statement stringWebThe essential dimension of a linear algebraic group G is always finite and bounded by the minimal dimension of a generically free representation minus the dimension of G. For … dhccare officialWeb3 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 … dhc cateringWeb10 de jul. de 2024 · arXivLabs: experimental projects with community collaborators. arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. dhc cash dropper