Definable and pseudofinite groups
The EU-funded DEFGROUP project is exploring logic (model theory) and algebra (group theory), by studying groups known as 'first-order definable' in structures that satisfy certain model-theoretic restrictions. The project is working to show that groups definable in tame fields are closely related to the rational points of an algebraic group. The project is also working to prove that the soluble radical of any pseudofinite group with a simple theory is soluble. The project also aims to demonstrate that any infinite group definable in a pseudofinite field (or in any pseudofinite structure) is pseudofinite.