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

Кафедра алгебры и математической логики ММФ

Результат исследования: Научные публикации в периодических изданиях › статья › рецензирование

Аннотация

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.

Язык оригинала	английский
Страницы (с-по)	154-159
Число страниц	6
Журнал	Algebra and Logic
Том	60
Номер выпуска	2
DOI	https://doi.org/10.1007/s10469-021-09637-9
Состояние	Опубликовано - мая 2021

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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.",

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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.

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KW - finite nilpotent group

KW - k-closure

KW - Sylow subgroup

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JO - Algebra and Logic

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SN - 0002-5232

IS - 2

ER -

Structure of k-Closures of Finite Nilpotent Permutation Groups

Аннотация

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