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 -