I am a Heilbronn Research Fellow at the University of Bristol. My research area is group theory. Until March 2019 I was a PhD student at the University of Bath.
My PhD introduced the notion of a Powerfully Nilpotent Group. This is a powerful p-group with a special kind of central series. It turns out (fortunately for my PhD), that these groups have a rich and interesting structure theory.
Please feel free to email me at the following address. I am always happy to discuss finite p-groups.
During my Heilbronn fellowship I plan to further develop the theory of Powerfully Nilpotent Groups, which I introduced during my PhD. I am also interested more generally in families of p-groups which are in some sense "close" to abelian groups (for instance regular p-groups and powerful p-groups). The behaviour of p-groups in general is well known to be wild, and so I believe it is profitable to find families of p-groups with nice properties, and then attempt to reduce questions about p-groups to these families.
I am also very interested in Experimental Mathematics. I make extensive use of the computational algebra system, GAP, to help formulate and refine conjectures. In fact I could not imagine research without it!
If your research interests are similar to mine, then please feel free to get in touch.
Where possible I will provide a link to an open access version of the article or a pre-print on Arxiv.
G. Traustason and J. Williams, Powerfully nilpotent groups of maximal powerful class, J. Monatsh Math, (2019)
J. Williams, Normal Subgroups of Powerful p-groups, Israel J. Math, to appear. Arxiv.
J. Williams, Quasi-powerful p-groups. Arxiv.
G. Traustason and J. Williams, Powerfully nilpotent groups of rank 2 or small order. Arxiv.