I’m please to announce that I’ve rereleased my PhD thesis and it is free to download on Leanpub.

Here is the preface.

Preface to the New Edition

Why revise a PhD thesis from almost 26 years ago? I guess I needed to scratch an itch and have a nostalgic review of the past.

I submitted this thesis in 2000 for a PhD in Pure Mathematics at the University of London. I studied under Prof. B. A. F. Wehrfritz at Queen Mary, University of London. Prof. P. M. Neumann and Prof. P. Flavell were my examiners. I had some corrections to make, but I successfully obtained my PhD in November 2000. And aside from writing up the results for publication, that is where my mathematical career stopped.

I have translated the text from LaTeX into Leanpub’s Markua 0.31 flavour of markdown. The AI agents Claude and Hermes assisted me. Claude read the implementation code and told me how to change some difficult mathematics. As I did the translation, I got Hermes and Claude to regularly check the text for formatting problems. They also compared it to the original PDF for differences. In the good old days, you would be lucky if a colleague would proofread your text once. In 2026, AI will read your text as many times as you like.

Then I drew a line in the sand and reread the text myself. I enjoyed reading the text for many reasons. There were comments in the text I’d left to my future self. There was the realisation that I couldn’t remember what I’d done all those years ago. There was the stirring of memories of being in an academic environment, one that is different to the “real world”.

I have made revisions, including:

  1. I’ve given it a new cover.
  2. I’ve changed the size so that it will fit nicely on a shelf when printed.
  3. I’ve fixed some errors in the text that Claude and I found.
  4. In the submitted PhD, instead of S-Engel elements I called them Sengel elements. My undergraduate tutor and the reviewer of the paper [C] said I should change it. I intended no disrespect to Engel, but I’ve updated this edition to use the terminology in the paper.

The results in this thesis appeared as four papers:

[A] C. J. E. Pinnock, Irreducible and Transitive Locally-Nilpotent by Abelian Finitary Groups, Arch. Math. 74 (2000) pp168-172.

[B] C. J. E. Pinnock, Lawlessness and Rank Restrictions in Certain Finitary Groups, Proc. Amer. Math. Soc. 130 (2002) pp2815-2819.

[C] C. J. E. Pinnock, Generalized Engel Elements in Group Theory, J. Group Theory 6 No. 1 (2003) pp69-81.

[D] C. J. E. Pinnock, Local Systems of Locally Supersoluble Finitary Groups, Glasgow Math. J. 45 (2003) pp239-242.

I dedicate this edition to Patrick Moss. Patrick (or Pat) was my A-level mathematics teacher. Pat had a knack for instilling a deep understanding of mathematical concepts. I still recall the first lessons where he taught differential calculus. If Pat hadn’t taught me, I would probably have done a Computer Science degree instead of a Mathematics one. He was a proficient mathematician himself and resumed his studies for a PhD in later life. Pat sadly passed away in March 2024.