## Abstract

We say that a finite group G acting on a set Ω has Property (⁎)_{p} for a prime p if P_{ω} is a Sylow p-subgroup of G_{ω} 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 A_{n} and symmetric group S_{n} 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 language | English |
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Pages (from-to) | 107-133 |

Number of pages | 27 |

Journal | Journal of Algebra |

Volume | 607 |

Early online date | 29 Jun 2021 |

DOIs | |

Publication status | Published - 1 Oct 2022 |