Structure of k-Closures of Finite Nilpotent Permutation Groups

D. V. Churikov

doi:10.1007/s10469-021-09637-9

Structure of k-Closures of Finite Nilpotent Permutation Groups

D. V. Churikov

Section of Algebra and Mathematical Logic

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

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 Ω^k. 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.

Original language	English
Pages (from-to)	154-159
Number of pages	6
Journal	Algebra and Logic
Volume	60
Issue number	2
DOIs	https://doi.org/10.1007/s10469-021-09637-9
Publication status	Published - May 2021

Keywords

finite nilpotent group
k-closure
Sylow subgroup

OECD FOS+WOS

1.01 MATHEMATICS

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10.1007/s10469-021-09637-9

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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.",

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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.",

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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

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JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 2

ER -

Structure of k-Closures of Finite Nilpotent Permutation Groups

Abstract

Keywords

OECD FOS+WOS

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