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Finite skew braces with solvable additive group. / Gorshkov, Ilya; Nasybullov, Timur.

в: Journal of Algebra, Том 574, 15.05.2021, стр. 172-183.

Результаты исследований: Научные публикации в периодических изданияхстатьяРецензирование

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Gorshkov I, Nasybullov T. Finite skew braces with solvable additive group. Journal of Algebra. 2021 май 15;574:172-183. doi: 10.1016/j.jalgebra.2021.01.027

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Gorshkov, Ilya ; Nasybullov, Timur. / Finite skew braces with solvable additive group. в: Journal of Algebra. 2021 ; Том 574. стр. 172-183.

BibTeX

@article{3a4633d1ad49495c980131cc8f6be85e,
title = "Finite skew braces with solvable additive group",
abstract = "A. Smoktunowicz and L. Vendramin conjectured that if A is a finite skew brace with solvable additive group, then the multiplicative group of A is solvable. In this short note we make a step towards positive solution of this conjecture proving that if A is a minimal finite skew brace with solvable additive group and non-solvable multiplicative group, then the multiplicative group of A is not simple. On the way to obtaining this result, we prove that the conjecture of A. Smoktunowicz and L. Vendramin is correct in the case when the order of A is not divisible by 3.",
keywords = "Simple group, Skew brace, Solvable group",
author = "Ilya Gorshkov and Timur Nasybullov",
note = "Funding Information: Acknowledgment. The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: {\textcopyright} 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.",
year = "2021",
month = may,
day = "15",
doi = "10.1016/j.jalgebra.2021.01.027",
language = "English",
volume = "574",
pages = "172--183",
journal = "Journal of Algebra",
issn = "0021-8693",
publisher = "Academic Press Inc.",

}

RIS

TY - JOUR

T1 - Finite skew braces with solvable additive group

AU - Gorshkov, Ilya

AU - Nasybullov, Timur

N1 - Funding Information: Acknowledgment. The work is supported by Mathematical Center in Akademgorodok under agreement No. 075-15-2019-1613 with the Ministry of Science and Higher Education of the Russian Federation. Publisher Copyright: © 2021 Elsevier Inc. Copyright: Copyright 2021 Elsevier B.V., All rights reserved.

PY - 2021/5/15

Y1 - 2021/5/15

N2 - A. Smoktunowicz and L. Vendramin conjectured that if A is a finite skew brace with solvable additive group, then the multiplicative group of A is solvable. In this short note we make a step towards positive solution of this conjecture proving that if A is a minimal finite skew brace with solvable additive group and non-solvable multiplicative group, then the multiplicative group of A is not simple. On the way to obtaining this result, we prove that the conjecture of A. Smoktunowicz and L. Vendramin is correct in the case when the order of A is not divisible by 3.

AB - A. Smoktunowicz and L. Vendramin conjectured that if A is a finite skew brace with solvable additive group, then the multiplicative group of A is solvable. In this short note we make a step towards positive solution of this conjecture proving that if A is a minimal finite skew brace with solvable additive group and non-solvable multiplicative group, then the multiplicative group of A is not simple. On the way to obtaining this result, we prove that the conjecture of A. Smoktunowicz and L. Vendramin is correct in the case when the order of A is not divisible by 3.

KW - Simple group

KW - Skew brace

KW - Solvable group

UR - http://www.scopus.com/inward/record.url?scp=85100437429&partnerID=8YFLogxK

U2 - 10.1016/j.jalgebra.2021.01.027

DO - 10.1016/j.jalgebra.2021.01.027

M3 - Article

AN - SCOPUS:85100437429

VL - 574

SP - 172

EP - 183

JO - Journal of Algebra

JF - Journal of Algebra

SN - 0021-8693

ER -

ID: 27708194