Closures of permutation groups with restricted nonabelian composition factors

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Closures of permutation groups with restricted nonabelian composition factors. / Ponomarenko, Ilia; Skresanov, Saveliy V.; Vasil'ev, Andrey V.

In: Bulletin of Mathematical Sciences, 2025.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{4990e2a52a8c4dbea5f0ae218943022b,

title = "Closures of permutation groups with restricted nonabelian composition factors",

abstract = "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.",

keywords = "k -closure, Alt ( d ) -free group, Permutation group",

author = "Ilia Ponomarenko and Skresanov, {Saveliy V.} and Vasil'ev, {Andrey V.}",

year = "2025",

doi = "10.1142/s1664360725500122",

language = "English",

journal = "Bulletin of Mathematical Sciences",

issn = "1664-3607",

publisher = "Springer Basel AG",

}

RIS

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