Grouping the important variables
The Classification of Finite Simple Groups (CFSG), also known as the 'enormous theorem', describes the basic building blocks of finite groups, just as prime numbers are the building blocks of natural numbers. Proof of the CFSG covers more than 10 000 journal pages. Group theory, one of modern mathematics' oldest branches, has connections with theories of representation and coding, as well as with combinatorics, algebraic geometry, physics and chemistry. The Marie Curie Fellowship project 'The non-coprime k(GV) problem and generation of finite groups' (Groups) has the goal of discovering applications in pure mathematics of the CFSG. The fellow, as a first step in this direction, performed work on the non-coprime k(GV)-problem, the results of which are being prepared for publication in collaboration with a fellow researcher at the host institute in Hungary. Other work succeeded in offering various applications and addressing the 1966 conjecture of Neumann related to the existence of elements in an irreducible linear group with small fixed space. The research also generalised a recent theorem on fixed-point spaces by Isaacs, Keller, Meierfrankenfeld and Moreto. The fellow, whose work also aims to boost Hungary's mathematical profile, has so far also made progress in work on the generation of finite groups. As the Groups project continues, the fellow is also receiving advanced training in extremal graph theory and in combinatorics.