A note on extremely primitive affine groups

Timothy C Burness, Adam R Thomas

Research output: Contribution to journalArticle (Academic Journal)

Abstract

Let G be a finite primitive permutation group on a set Ω with nontrivial point stabilizer Gα. We say that G is extremely primitive if Gα acts primitively on each of its orbits in Ω \ {α}. In earlier work, Mann, Praeger and Seress have proved that every extremely primitive group is either almost simple or of affine type and they have classified the affine groups up to the possibility of at most finitely many exceptions. More recently, the almost simple extremely primitive groups have been completely determined. If one assumes Wall’s conjecture on the number of maximal subgroups of almost simple groups, then the results of Mann et al. show that it just remains to eliminate an explicit list of affine groups in order to complete the classification of the extremely primitive groups. Mann et al. have conjectured that none of these affine candidates are extremely primitive and our main result confirms this conjecture.
Original languageEnglish
Number of pages8
JournalArchiv der Mathematik
Publication statusAccepted/In press - 31 Aug 2020

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