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Structure of k-Closures of Finite Nilpotent Permutation Groups. / Churikov, D. V.

In: Algebra and Logic, Vol. 60, No. 2, 05.2021, p. 154-159.

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

Harvard

Churikov, DV 2021, 'Structure of k-Closures of Finite Nilpotent Permutation Groups', Algebra and Logic, vol. 60, no. 2, pp. 154-159. https://doi.org/10.1007/s10469-021-09637-9

APA

Churikov, D. V. (2021). Structure of k-Closures of Finite Nilpotent Permutation Groups. Algebra and Logic, 60(2), 154-159. https://doi.org/10.1007/s10469-021-09637-9

Vancouver

Churikov DV. Structure of k-Closures of Finite Nilpotent Permutation Groups. Algebra and Logic. 2021 May;60(2):154-159. doi: 10.1007/s10469-021-09637-9

Author

Churikov, D. V. / Structure of k-Closures of Finite Nilpotent Permutation Groups. In: Algebra and Logic. 2021 ; Vol. 60, No. 2. pp. 154-159.

BibTeX

@article{3cd810a3e32f4c57a381c77ec0992d89,
title = "Structure of k-Closures of Finite Nilpotent Permutation Groups",
abstract = "Let G be a permutation group of a set Ω and k be a positive integer. The k-closure of G is the greatest (w.r.t. inclusion) subgroup G(k) in Sym(Ω) which has the same orbits as has G under the componentwise action on the set Ωk. It is proved that the k-closure of a finite nilpotent group coincides with the direct product of k-closures of all of its Sylow subgroups.",
keywords = "finite nilpotent group, k-closure, Sylow subgroup",
author = "Churikov, {D. V.}",
note = "Funding Information: Supported by Mathematical Center in Akademgorodok, Agreement with RF Ministry of Education and Science No. 075-15-2019-1613. Publisher Copyright: {\textcopyright} 2021, Springer Science+Business Media, LLC, part of Springer Nature.",
year = "2021",
month = may,
doi = "10.1007/s10469-021-09637-9",
language = "English",
volume = "60",
pages = "154--159",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "2",

}

RIS

TY - JOUR

T1 - Structure of k-Closures of Finite Nilpotent Permutation Groups

AU - Churikov, D. V.

N1 - Funding Information: Supported by Mathematical Center in Akademgorodok, Agreement with RF Ministry of Education and Science No. 075-15-2019-1613. Publisher Copyright: © 2021, Springer Science+Business Media, LLC, part of Springer Nature.

PY - 2021/5

Y1 - 2021/5

N2 - Let G be a permutation group of a set Ω and k be a positive integer. The k-closure of G is the greatest (w.r.t. inclusion) subgroup G(k) in Sym(Ω) which has the same orbits as has G under the componentwise action on the set Ωk. It is proved that the k-closure of a finite nilpotent group coincides with the direct product of k-closures of all of its Sylow subgroups.

AB - Let G be a permutation group of a set Ω and k be a positive integer. The k-closure of G is the greatest (w.r.t. inclusion) subgroup G(k) in Sym(Ω) which has the same orbits as has G under the componentwise action on the set Ωk. It is proved that the k-closure of a finite nilpotent group coincides with the direct product of k-closures of all of its Sylow subgroups.

KW - finite nilpotent group

KW - k-closure

KW - Sylow subgroup

UR - http://www.scopus.com/inward/record.url?scp=85115135617&partnerID=8YFLogxK

U2 - 10.1007/s10469-021-09637-9

DO - 10.1007/s10469-021-09637-9

M3 - Article

AN - SCOPUS:85115135617

VL - 60

SP - 154

EP - 159

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 2

ER -

ID: 34257315