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