The (7,4)-conjecture in finite groups

2013/08/31 by Jozsef Solymosi, Solymosi, Jozsef · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR

paper · pdf · doi:10.48550/arxiv.1309.0133

arxiv created 2013/08/31 · arxiv updated 2013/09/03

Abstract

The first open case of the Brown, Erdős, Sós conjecture is equivalent to the following; For every c>0 there is a threshold n₀ so that if a quasigroup has order n≥ n₀ then for every subset of triples of the form (a,b,ab), denoted by S, if |S|≥ cn² then there is a seven-element subset of the quasigroup which spans at least four triples of the selected subset S. In this paper we prove the conjecture for finite groups.

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