Zoltán Halasi: On the base size of primitive permutation groups.

Speaker: Zoltán Halasi

Title: On the base size of primitive permutation groups.

Abstract: LetG≤Sym(Ω)  be  a  finite  permutation  group.   A  subsetX⊂Ω  iscalled  a  base  forGif  the  pointwise  stabilizer  ofXinGis  trivial.   Theminimal  size  of  a  base  forGis  denoted  byb(G).   It  is  easy  to  see  thatlog|G|/log|Ω| ≤b(G) holds for any permutation group.  Pyber asked in a1993 paper whether this formula is essentially sharp for the base size of aprimitive permutation group, i.e.  whether there exists a universal constantcsuch thatb(G)≤clog|G|/log|Ω|holds for any primitive permutation group.Previous results reduced this problem to permutation groups of affine type.In this talk, we sketch the proof of this case.A joint work with H ̈ulya Duyan and Attila Maróti.