Around 25-30 years ago, I was fascinated by the group structure of the Rubik’s cube group (whose size is roughly 4.3×10^19). It turns out (see my book on the Rubik’s cube for details) to be simply described using generalized symmetric groups. As a result, I wanted to know more about their representations and this lead to the question, what is the smallest field over which you can faithfully represent the generalized symmetric group (as matrices)? This lead to some lecture notes in 1998 and then a more refined preprint in 2002. After revisions, this was published in Archiv der Mathematik, vol 81 (2003)113–120.

What did AI think of this paper? While it found no serious errors (the main results and proofs were correct), Opus-Claude found an incorrect statement and that I’d mis-stated a result due to J.P. Serre. So I asked AI to write a more readable corrected version, adding a Glossary, Further directions paragraph, Literature review, and a Summary section. The corrected revision is here (11 page pdf). Hope you enjoy reading it as much as I did writing it!