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.
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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) ≥ ...
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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.
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Let $G$ be a finite group. A subset $X$ of $G$ is a set of pairwise non-commuting elements if any two distinct elements of $X$ do not commute. In this paper we determine the maximum size of these subsets in any finite non-abelian metacyclic $2$-group and in any finite non-abelian $p$-group with an abelian maximal subgroup.
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ژورنال
عنوان ژورنال: Commentarii Mathematici Helvetici
سال: 2013
ISSN: 0010-2571
DOI: 10.4171/cmh/296