An Ennola duality for subgroups of groups of Lie type

David A. Craven, University of Birmingham

23rd August, 2022

I distinguish four types of corrections, in order of increasing seriousness:

  • (Extra) Additional information that was not available at the time of writing, or that I did not know about.

  • (Improve) Typographical issues, where what is written is still correct, but there is a nicer way of phrasing it, or I could choose a better symbol.

  • (Typo) Typographical errors, where I have spelled a word wrongly, used the wrong symbol, and so on.

  • (Error) Errors in proofs or statements.

When I give each correction, I will label it with one of these monikers.

  • (i) (Error) At the start of Section 3.1, the remark that the discriminant is odd appears to be true, but the ‘proof’ that is given in the text is fallacious.

  • (ii) (Extra) Surprisingly, Conjecture 3.9 seems to have a negative answer. I only say seems to have because the counterexample is so large that it cannot be directly checked, and theorems are needed. The O’Nan group in dimension 169290 is a counterexample, according to the results of Nebe and Parker in [1, Remark 7.3].

References

  • [1]  Gabriele Nebe and Richard Parker, Orthogonal stability, 2022. arXiv:2203.03202