@article{5aa3add88c37463f8d28a0388ac3506d,
title = "The 3-closure of a solvable permutation group is solvable",
abstract = "Let m be a positive integer and let Ω be a finite set. The m-closure of G≤Sym(Ω) is the largest permutation group on Ω having the same orbits as G in its induced action on the Cartesian product Ωm. The 1-closure and 2-closure of a solvable permutation group need not be solvable. We prove that the m-closure of a solvable permutation group is always solvable for m≥3.",
keywords = "Finite groups, m-closure, Permutation groups",
author = "O'Brien, {E. A.} and I. Ponomarenko and Vasil'ev, {A. V.} and E. Vdovin",
note = "Funding Information: O'Brien was supported by the Marsden Fund of New Zealand grant UOA 107 ; Ponomarenko and Vasil'ev were supported by the Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation ; Vdovin was supported by the RFBR grant No. 18-01-00752 . We thank the referee for helpful feedback. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc.",
year = "2021",
month = jul,
day = "13",
doi = "10.1016/j.jalgebra.2021.07.002",
language = "English",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",
}