James Williams

Abelian-like properties in p-groups

An important idea in the theory of p-groups has been finding families with desirable properties, such as those enjoyed by abelian groups. In this light we consider groups which are 'powerful' in the sense of Lubotzky and Mann. We introduce a new family of powerful groups called 'powerfully nilpotent' groups and explore some of their most interesting properties.

With the aim of making this talk as accessible as possible, we will begin by recalling some basic properties of p-groups and motivation for studying them.

The theory of powerful nilpotence was developed together with Gunnar Traustason.