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I came across a reference in this MathOverflow answer to an intriguing result of Ulrich Felgner [1]: among finite non-Abelian groups, the property of being simple is first-order definable. According to that answer, he derives it as a consequence of the classification of finite simple groups (which seems very plausible, but tantalising).

I would be interested to see a proof of this result — either Felgner’s original paper [1], or (especially) if there have been any subsequent alternative proofs given, especially not relying on the CFSG. Unfortunately I’ve been unable to access a copy of [1] — I can only find physical holdings at a few libraries in Germany (list on WorldCat) — nor any other presentations of the result. Hence my main question: Can anyone recommend a physically/electronically accessible reference for Felgner’s result? I’d be happy with either Felgner’s original [1] or any subsequent work, and either electronic access or a more widely-distributed physical version.

References:

  1. Ulrich Felgner, Pseudo-endliche Gruppen. (Pseudofinite groups), MR1107758, Proceedings of the 8th Easter Conference on Model Theory (Wendisch-Rietz, 1990), 82–96, Seminarberichte, 110, Humboldt Univ., Berlin, 1990.
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    $\begingroup$ These 2019 slides by John Wilson, esp slide 9, provide more information and context: mat.polsl.pl/groups/binn/wilson.pdf $\endgroup$
    – user44143
    Sep 13, 2022 at 1:37

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