Corrigendum and addendum to "Transitive permutation groups where nontrivial elements have at most two fixed points"

TL;DR

This paper corrects minor errors in previous work on transitive permutation groups with elements fixing at most two points, confirming that core results and classifications remain valid, and provides supplementary GAP code.

Contribution

It provides corrections to earlier results on permutation groups and includes new computational tools, ensuring the robustness of the main classification results.

Findings

Errors in earlier results are minor and do not affect main theorems.

Classification of simple groups with fixity 2 remains valid.

GAP code is added for computational verification.

Abstract

This article revisits earlier work by the second author together with Kay Magaard. We correct several little results and we briefly discuss why, fortunately, the errors hardly affect our main theorems and in particular do not affect the classification of simple groups that act with fixity 2. As an addition to the submitted article, this version also contains GAP code in a little appendix at the end.