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Factoring nonabelian finite groups into two subsets. / Bildanov, R. R.; Goryachenko, V. A.; Vasil'ev, A. V.

In: Сибирские электронные математические известия, Vol. 17, 01.05.2020, p. 683-689.

Research output: Contribution to journalArticlepeer-review

Harvard

Bildanov, RR, Goryachenko, VA & Vasil'ev, AV 2020, 'Factoring nonabelian finite groups into two subsets', Сибирские электронные математические известия, vol. 17, pp. 683-689. https://doi.org/10.33048/semi.2020.17.046

APA

Bildanov, R. R., Goryachenko, V. A., & Vasil'ev, A. V. (2020). Factoring nonabelian finite groups into two subsets. Сибирские электронные математические известия, 17, 683-689. https://doi.org/10.33048/semi.2020.17.046

Vancouver

Bildanov RR, Goryachenko VA, Vasil'ev AV. Factoring nonabelian finite groups into two subsets. Сибирские электронные математические известия. 2020 May 1;17:683-689. doi: 10.33048/semi.2020.17.046

Author

Bildanov, R. R. ; Goryachenko, V. A. ; Vasil'ev, A. V. / Factoring nonabelian finite groups into two subsets. In: Сибирские электронные математические известия. 2020 ; Vol. 17. pp. 683-689.

BibTeX

@article{bddb103e216e4fc5a9dc21d65781061e,
title = "Factoring nonabelian finite groups into two subsets",
abstract = "A group G is said to be factorized into subsets A1, A2,..., As ⊆ G if every element g in G can be uniquely represented as g = g1g2... gs, where gi ∈ Ai, i = 1, 2,..., s. We consider the following conjecture: for every finite group G and every factorization n = ab of its order, there is a factorization G = AB with |A| = a and |B| = b. We show that a minimal counterexample to this conjecture must be a nonabelian simple group and prove the conjecture for every finite group the nonabelian composition factors of which have orders less than 10 000.",
keywords = "Factoring of groups into subsets, Finite group, Finite simple group, Maximal subgroups, finite group, factoring of groups into subsets, maximal subgroups, finite simple group",
author = "Bildanov, {R. R.} and Goryachenko, {V. A.} and Vasil'ev, {A. V.}",
note = "Publisher Copyright: {\textcopyright} 2020 Bildanov R.R., Goryachenko V.A., Vasil'ev A.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.",
year = "2020",
month = may,
day = "1",
doi = "10.33048/semi.2020.17.046",
language = "English",
volume = "17",
pages = "683--689",
journal = "Сибирские электронные математические известия",
issn = "1813-3304",
publisher = "Sobolev Institute of Mathematics",

}

RIS

TY - JOUR

T1 - Factoring nonabelian finite groups into two subsets

AU - Bildanov, R. R.

AU - Goryachenko, V. A.

AU - Vasil'ev, A. V.

N1 - Publisher Copyright: © 2020 Bildanov R.R., Goryachenko V.A., Vasil'ev A.V. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/5/1

Y1 - 2020/5/1

N2 - A group G is said to be factorized into subsets A1, A2,..., As ⊆ G if every element g in G can be uniquely represented as g = g1g2... gs, where gi ∈ Ai, i = 1, 2,..., s. We consider the following conjecture: for every finite group G and every factorization n = ab of its order, there is a factorization G = AB with |A| = a and |B| = b. We show that a minimal counterexample to this conjecture must be a nonabelian simple group and prove the conjecture for every finite group the nonabelian composition factors of which have orders less than 10 000.

AB - A group G is said to be factorized into subsets A1, A2,..., As ⊆ G if every element g in G can be uniquely represented as g = g1g2... gs, where gi ∈ Ai, i = 1, 2,..., s. We consider the following conjecture: for every finite group G and every factorization n = ab of its order, there is a factorization G = AB with |A| = a and |B| = b. We show that a minimal counterexample to this conjecture must be a nonabelian simple group and prove the conjecture for every finite group the nonabelian composition factors of which have orders less than 10 000.

KW - Factoring of groups into subsets

KW - Finite group

KW - Finite simple group

KW - Maximal subgroups

KW - finite group

KW - factoring of groups into subsets

KW - maximal subgroups

KW - finite simple group

UR - http://www.scopus.com/inward/record.url?scp=85087778532&partnerID=8YFLogxK

U2 - 10.33048/semi.2020.17.046

DO - 10.33048/semi.2020.17.046

M3 - Article

AN - SCOPUS:85087778532

VL - 17

SP - 683

EP - 689

JO - Сибирские электронные математические известия

JF - Сибирские электронные математические известия

SN - 1813-3304

ER -

ID: 24768784