Orbits of Sylow subgroups of finite permutation groups

2021/01/31 by Bamberg, John, Bors, Alexander, Devillers, Alice +3 · 1 citation
#20B05 #20B15 #FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2102.00448

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.

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• Derangements in permutation groups with two orbits

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