Simple finite group schemes and their infinitesimal deformations

We show that the classification of simple finite group schemes over an algebraically closed field reduces to the classification of abstract simple finite groups and of simple restricted Lie algebras in positive characteristic. Both these two simple objects have been classified. We review this classification. Finally, we address the problem of determining the infinitesimal deformations of simple finite group schemes. Mathematics Subject Classification: 14L15, 17B70, 20D05, 17B50, 17B56.