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The 3-closure of a solvable permutation group is solvable. / O'Brien, E. A.; Ponomarenko, I.; Vasil'ev, A. V. и др.
в: Journal of Algebra, Том 607, 01.10.2022, стр. 618-637.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - The 3-closure of a solvable permutation group is solvable
AU - O'Brien, E. A.
AU - Ponomarenko, I.
AU - Vasil'ev, A. V.
AU - Vdovin, E.
N1 - 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: © 2021 Elsevier Inc.
PY - 2022/10/1
Y1 - 2022/10/1
N2 - 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.
AB - 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.
KW - Finite groups
KW - m-closure
KW - Permutation groups
UR - http://www.scopus.com/inward/record.url?scp=85110998304&partnerID=8YFLogxK
U2 - 10.1016/j.jalgebra.2021.07.002
DO - 10.1016/j.jalgebra.2021.07.002
M3 - Article
AN - SCOPUS:85110998304
VL - 607
SP - 618
EP - 637
JO - Journal of Algebra
JF - Journal of Algebra
SN - 0021-8693
ER -
ID: 34108115