# James Williams - University of Bristol

## Summary

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.

## Contact

Please feel free to email me at the following address. I am always happy to discuss finite p-groups.

## Research Interests

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*.

## Publications

*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, J. Algebra, 522(2019), 80-100. Arxiv.

J. Williams, Omegas of Agemos in Powerful Groups, Int. J. Group Theory, to appear (early online access available since March 2019). 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.