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Closures of permutation groups with restricted nonabelian composition factors. / Ponomarenko, Ilia; Skresanov, Saveliy V.; Vasil'ev, Andrey V.
в: Bulletin of Mathematical Sciences, 2025.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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TY - JOUR
T1 - Closures of permutation groups with restricted nonabelian composition factors
AU - Ponomarenko, Ilia
AU - Skresanov, Saveliy V.
AU - Vasil'ev, Andrey V.
PY - 2025
Y1 - 2025
N2 - Given a permutation group G on a finite set Ω, let G(k) denote the k-closure of G, thatis, the largest permutation group on Ω having the same orbits in the induced action onΩk as G. Recall that a group is Alt(d)-free if it does not contain a section isomorphic tothe alternating group of degree d. Motivated by some problems in computational grouptheory, we prove that the k-closure of an Alt(d)-free group is again Alt(d)-free for k ≥ 4and d ≥ 25.
AB - Given a permutation group G on a finite set Ω, let G(k) denote the k-closure of G, thatis, the largest permutation group on Ω having the same orbits in the induced action onΩk as G. Recall that a group is Alt(d)-free if it does not contain a section isomorphic tothe alternating group of degree d. Motivated by some problems in computational grouptheory, we prove that the k-closure of an Alt(d)-free group is again Alt(d)-free for k ≥ 4and d ≥ 25.
KW - k -closure
KW - Alt ( d ) -free group
KW - Permutation group
UR - https://www.mendeley.com/catalogue/b5b08686-2e07-3cd6-9bba-d407fc1545dd/
UR - https://www.scopus.com/inward/record.uri?partnerID=HzOxMe3b&scp=105009489164&origin=inward
U2 - 10.1142/s1664360725500122
DO - 10.1142/s1664360725500122
M3 - Article
JO - Bulletin of Mathematical Sciences
JF - Bulletin of Mathematical Sciences
SN - 1664-3607
M1 - 255012
ER -
ID: 68292441