Orbits of Sylow subgroups of finite permutation groups

被引:0
作者
Bamberg, John [1 ]
Bors, Alexander [2 ]
Devillers, Alice [1 ]
Giudici, Michael [1 ]
Praeger, Cheryl E. [1 ]
Royle, Gordon F. [1 ]
机构
[1] Univ Western Australia, Ctr Math Symmetry & Computat, Dept Math & Stat, Crawley, WA 6009, Australia
[2] Carleton Univ, Sch Math & Stat, 1125 Colonel By Dr, Ottawa, ON K1S 5B6, Canada
基金
奥地利科学基金会;
关键词
Permutation groups; Primitive groups; Sylow subgroups; ELEMENTS; ODD;
D O I
10.1016/j.jalgebra.2021.06.017
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We say that a finite group G acting on a set Omega has Property (*)(p) for a prime p if P-omega is a Sylow p-subgroup of G(omega) for all omega is an element of Omega 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 primep. (c) 2021 Elsevier Inc. All rights reserved.
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页码:107 / 133
页数:27
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