Geodesic
On base sizes for algebraic groups
Journal of the European Mathematical Society, Tome 19 (2017) no. 8, pp. 2269-2341.

Voir la notice de l'article provenant de la source EMS Press

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 
@article{JEMS_2017_19_8_a2,
     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},
     publisher = {mathdoc},
     volume = {19},
     number = {8},
     year = {2017},
     doi = {10.4171/jems/718},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/718/}
}
TY  - JOUR
AU  - Timothy C. Burness
AU  - Robert M. Guralnick
AU  - Jan Saxl
TI  - On base sizes for algebraic groups
JO  - Journal of the European Mathematical Society
PY  - 2017
SP  - 2269
EP  - 2341
VL  - 19
IS  - 8
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.4171/jems/718/
DO  - 10.4171/jems/718
ID  - JEMS_2017_19_8_a2
ER  - 
%0 Journal Article
%A Timothy C. Burness
%A Robert M. Guralnick
%A Jan Saxl
%T On base sizes for algebraic groups
%J Journal of the European Mathematical Society
%D 2017
%P 2269-2341
%V 19
%N 8
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.4171/jems/718/
%R 10.4171/jems/718
%F JEMS_2017_19_8_a2
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. http://geodesic.mathdoc.fr/articles/10.4171/jems/718/

Cité par Sources :