Schemes with the base of size 2

Andrey Vasil\'ev
Sobolev Institute of Mathematics, Novosibirsk, Russia

Ilya Ponomarenko
Saint Petersburg Department of V. A. Steklov Institute of Mathematics, Russia



Content: A sufficient condition for a homogeneous coherent configuration (or simply a scheme) to have the (combinatorial) base of size $2$ is proved. This result is applied to the Cartan scheme of a finite simple group $G$ with BN-pair; by definition, it is the coherent configuration associated with the action of $G$ on the right cosets of the Cartan subgroup $H=B\cap N$ by the right multiplications.

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