**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**

**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 a freely available pre-print or open access version of the article. *

**G. Traustason and J.
Williams, ****Powerfully
nilpotent groups ****, J.
Algebra , 522 (2019), 80-100.**

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

**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. **

**J. Williams, Quasi-powerful p-groups, Arxiv Link**

*Last updated: October 2019*