Factoring nonabelian finite groups into two subsets

R. R. Bildanov, V. A. Goryachenko, A. V. Vasil'ev

Research output: Contribution to journalArticlepeer-review

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.

Original languageEnglish
Pages (from-to)683-689
Number of pages7
JournalСибирские электронные математические известия
Volume17
DOIs
Publication statusPublished - 1 May 2020

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

OECD FOS+WOS

  • 1.01 MATHEMATICS

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