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This article is cited in 2 scientific papers (total in 2 papers)
Mathematical logic, algebra and number theory
Factoring nonabelian finite groups into two subsets
R. R. Bildanova, V. A. Goryachenkob, A. V. Vasil'evc a Specialized Educational Scientific Center of Novosibirsk State University, 11/1, Pirogova str., Novosibirsk, 630090, Russia
b Novosibirsk State University, 1, Pirogova str., Novosibirsk, 630090, Russia
c Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia
Abstract:
A group $G$ is said to be factorized into subsets $A_1, A_2,$ $\ldots, A_s\subseteq G$ if every element $g$ in $G$ can be uniquely represented as $g=g_1g_2\ldots g_s$, where $g_i\in A_i$, $i=1,2,\ldots,s$. 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.
Received April 30, 2020, published May 21, 2020
Citation:
R. R. Bildanov, V. A. Goryachenko, A. V. Vasil'ev, “Factoring nonabelian finite groups into two subsets”, Sib. Èlektron. Mat. Izv., 17 (2020), 683–689
Linking options:
https://www.mathnet.ru/eng/semr1241 https://www.mathnet.ru/eng/semr/v17/p683
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