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The Closures of Wreath Products in Product Action. / Vasil’ev, A. V.; Ponomarenko, I. N.

In: Algebra and Logic, Vol. 60, No. 3, 07.2021, p. 188-195.

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

Harvard

Vasil’ev, AV & Ponomarenko, IN 2021, 'The Closures of Wreath Products in Product Action', Algebra and Logic, vol. 60, no. 3, pp. 188-195. https://doi.org/10.1007/s10469-021-09640-0

APA

Vasil’ev, A. V., & Ponomarenko, I. N. (2021). The Closures of Wreath Products in Product Action. Algebra and Logic, 60(3), 188-195. https://doi.org/10.1007/s10469-021-09640-0

Vancouver

Vasil’ev AV, Ponomarenko IN. The Closures of Wreath Products in Product Action. Algebra and Logic. 2021 Jul;60(3):188-195. doi: 10.1007/s10469-021-09640-0

Author

Vasil’ev, A. V. ; Ponomarenko, I. N. / The Closures of Wreath Products in Product Action. In: Algebra and Logic. 2021 ; Vol. 60, No. 3. pp. 188-195.

BibTeX

@article{6a1de89eb5a7485e9c12972a0d0ec7c1,
title = "The Closures of Wreath Products in Product Action",
abstract = "Let m be a positive integer and let Ω be a finite set. The m-closure of G ≤ Sym(Ω) is the largest permutation group G(m) on Ω having the same orbits as G in its induced action on the Cartesian product Ωm. An exact formula for the m-closure of the wreath product in product action is given. As a corollary, a sufficient condition is obtained for this m-closure to be included in the wreath product of the m-closures of the factors.",
keywords = "(1, 1)-superalgebra, left-symmetric algebra, Pierce decomposition, pre-Lie algebra, prime ring, right-symmetric ring",
author = "Vasil{\textquoteright}ev, {A. V.} and Ponomarenko, {I. N.}",
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 = jul,
doi = "10.1007/s10469-021-09640-0",
language = "English",
volume = "60",
pages = "188--195",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "3",

}

RIS

TY - JOUR

T1 - The Closures of Wreath Products in Product Action

AU - Vasil’ev, A. V.

AU - Ponomarenko, I. N.

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 - 2021/7

Y1 - 2021/7

N2 - Let m be a positive integer and let Ω be a finite set. The m-closure of G ≤ Sym(Ω) is the largest permutation group G(m) on Ω having the same orbits as G in its induced action on the Cartesian product Ωm. An exact formula for the m-closure of the wreath product in product action is given. As a corollary, a sufficient condition is obtained for this m-closure to be included in the wreath product of the m-closures of the factors.

AB - Let m be a positive integer and let Ω be a finite set. The m-closure of G ≤ Sym(Ω) is the largest permutation group G(m) on Ω having the same orbits as G in its induced action on the Cartesian product Ωm. An exact formula for the m-closure of the wreath product in product action is given. As a corollary, a sufficient condition is obtained for this m-closure to be included in the wreath product of the m-closures of the factors.

KW - (1, 1)-superalgebra

KW - left-symmetric algebra

KW - Pierce decomposition

KW - pre-Lie algebra

KW - prime ring

KW - right-symmetric ring

UR - http://www.scopus.com/inward/record.url?scp=85118576704&partnerID=8YFLogxK

U2 - 10.1007/s10469-021-09640-0

DO - 10.1007/s10469-021-09640-0

M3 - Article

AN - SCOPUS:85118576704

VL - 60

SP - 188

EP - 195

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 3

ER -

ID: 34607037