Let G be a connected and simply connected semisimple algebraic group over an algebraically closed field k of characteristic p > 0, T a maximal torus of G and B a Borel subgroup containing T . Each weight in X(T ) determines a line bundle on the flag varietyG/B. It turns out that cohomology of the line bundle is isomorphic to the derived functor of the induction functors from the category of B-m...

the main aim of this article is to study (v,k,λ)-symmetric designs admitting a flag-transitive and point-primitive automorphism group g whose socle is psl(3,q). we indeed show that the only possible design satisfying these conditions is a desarguesian projective plane pg(2,q) and g > psl(3,q).

The spectrum of a finite group is the set its element orders. We prove that if $$m>5$$ then $$L_{2^m}(2)\times L_{2^m}(2)\times L_{2^m}(2)$$ uniquely determined by in class groups.