### Saul Freedman

#### Thesis

Universal p-groups and p-groups related to exceptional groups of Lie type

#### Summary

The main aim of my research is to construct abstract p-groups that are related in a particular way to certain groups of matrices, where a p-group is a group whose order is a power of a prime p. More specifically, for each exceptional group of Lie type H defined over a field of odd prime order, I aim to construct a p-group P such that the group induced by the automorphism group of P on the Frattini quotient of P is a group related to H.

I also aim to construct new families of universal p-groups, which are the largest p-groups satisfying certain quantitative properties (namely, having a given nilpotency class, a given rank, and exponent p), and to explore the structures of their automorphism groups.

#### Why my research is important

My research will further the study of p-groups and exceptional groups of Lie type, which are very important in the context of finite group theory.

#### Funding

- Hackett Postgraduate Research Scholarship