Orbits of Sylow subgroups of finite permutation groups

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We say that a finite group G acting on a set Ω has Property (⁎)p for a prime p if Pω is a Sylow p-subgroup of Gω for all ω∈Ω and Sylow p-subgroups P of G. Property (⁎)p arose in the recent work of Tornier (2018) on local Sylow p-subgroups of Burger–Mozes groups, and he determined the values of p for which the alternating group An and symmetric group Sn acting on n points has Property (⁎)p. In this paper, we extend this result to finite 2-transitive groups and we give a structural characterisation result for the finite primitive groups that satisfy Property (⁎)p for an allowable prime p.

Original languageEnglish
Pages (from-to)107-133
Number of pages27
JournalJournal of Algebra
Early online date29 Jun 2021
Publication statusPublished - 1 Oct 2022


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