论文信息 - Essential Dimensions of A_7 and S_7 - 字舞流文

Essential Dimensions of A_7 and S_7

We show that Y. Prokhorov's ``Simple Finite Subgroups of the {C}remona Group of Rank 3'' implies that, over any field of characteristic $0$, the essential dimensions of the alternating group, $A_7$, and the symmetric group, $S_7$, are $4$.

Alexander Duncan

[1] Ju. Manin,et al. RATIONAL SURFACES OVER PERFECT FIELDS. II , 1967 .

[2] A. Ledet. Finite groups of essential dimension one , 2007 .

[3] J. Buhler,et al. On the essential dimension of a finite group , 1997, Compositio Mathematica.

[4] J. Conway,et al. ATLAS of Finite Groups , 1985 .

[5] Ju. Manin,et al. Rational surfaces over perfect fields , 1966 .

[6] Essential dimensions of finite groups , 2006, math/0611673.

[7] G. Berhuy,et al. Essential dimension: A functorial point of view (after A. Merkurjev) , 2003, Documenta Mathematica.

[8] Z. Reichstein,et al. Essential dimension and algebraic stacks , 2007, math/0701903.

[9] Joe Buhler,et al. On Tschirnhaus Transformations , 1999 .

[10] Zinovy Reichstein,et al. Essential Dimensions of Algebraic Groups and a Resolution Theorem for G-Varieties , 1999, Canadian Journal of Mathematics.

[11] Z. Reichstein. On the notion of essential dimension for algebraic groups , 2000 .

[12] Groups with Essential Dimension One , 2006, math/0611917.

[13] V A Iskovskih,et al. Minimal Models of Rational Surfaces Over Arbitrary Fields , 1980 .

[14] Nikita A. Karpenko,et al. Essential dimension of finite p-groups , 2008 .

[15] J. Conway,et al. Atlas of finite groups : maximal subgroups and ordinary characters for simple groups , 1987 .