Geodesic
On base sizes for algebraic groups
Journal of the European Mathematical Society, Tome 19 (2017) no. 8, pp. 2269-2341 Cet article a éte moissonné depuis la source EMS Press

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Let G be a permutation group on a set Ω. A subset of Ω is a base for G if its point-wise stabilizer is trivial; the base size of G is the minimal cardinality of a base. In this paper we initiate the study of bases for algebraic groups defined over an algebraically closed field. In particular, we calculate the base size for all primitive actions of simple algebraic groups, obtaining the precise value in almost all cases. We also introduce and study two new base measures, which arise naturally in this setting. We give an application concerning the essential dimension of simple algebraic groups, and we establish several new results on base sizes for the corresponding finite groups of Lie type. The latter results are an important contribution to the classical study of bases for finite primitive permutation groups. We also indicate some connections with generic stabilizers for representations of simple algebraic groups.
DOI : 10.4171/jems/718
Classification : 20-XX, 14-XX, 22-XX
Keywords: Base size, simple algebraic groups, primitive permutation groups, generic stabilizer 
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     author = {Timothy C. Burness and Robert M. Guralnick and Jan Saxl},
     title = {On base sizes for algebraic groups},
     journal = {Journal of the European Mathematical Society},
     pages = {2269--2341},
     year = {2017},
     volume = {19},
     number = {8},
     doi = {10.4171/jems/718},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/718/}
}
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Timothy C. Burness; Robert M. Guralnick; Jan Saxl. On base sizes for algebraic groups. Journal of the European Mathematical Society, Tome 19 (2017) no. 8, pp. 2269-2341. doi: 10.4171/jems/718

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