منابع مشابه
Essential Dimension of Finite Groups in Prime Characteristic
Let F be a eld of characteristic p > 0 and G be a smooth nite algebraic group over F . We compute the essential dimension edF (G; p) of G at p. That is, we show that edF (G; p) = { 1, if p divides |G|, and 0, otherwise.
متن کاملEssential dimensions of finite groups
Let K be an arbitrary field and G be a finite group. We will study the essential dimension of G over K, which is denoted by edK(G). A generalization of the central extension theorem of Buhler and Reichstein (Compositio Math. 106 (1997) 159–179, Theorem 5.3) is obtained. As a corollary, it can be proved that edK(Sn) ≥ ⌊ 2 ⌋ and edK(An) ≥ 2⌊ n 4 ⌋ for any field K with charK 6= 2, while edK(Sn) ≥ ...
متن کاملGroups of finite dimension in model theory
The Morley rank is the usual notion of dimension in model theory which encapsulates the more classical notion of dimension of algebraic varieties in algebraic geometry. In this paper we give a survey of results concerning the classification of infinite simple groups of finite Morley rank. We emphasize both the developments parallel to the Classification of the Finite Simple Groups and the incre...
متن کاملPseudo-reflection groups and essential dimension
We give a simple formula for the essential dimension of a finite pseudoreflection group at a prime p and determine the absolute essential dimension for most irreducible pseudo-reflection groups. We also study the “poor man’s essential dimension” of an arbitrary finite group, an intermediate notion between the absolute essential dimension and the essential dimension at a prime p.
متن کاملApplication of Multihomogeneous Covariants to the Essential Dimension of Finite Groups
We investigate essential dimension of finite groups over arbitrary fields and give a systematic treatment of multihomogenization, introduced in [KLS08]. We generalize the central extension theorem of Buhler and Reichstein, [BR97, Theorem 5.3] and use multihomogenization to substitute and generalize the stack-involved part of the theorem of Karpenko and Merkurjev [KM08] about the essential dimen...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2007
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2006.12.027