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The (7, 4)-Conjecture in Finite Groups

Part of: Extremal combinatorics Algebraic combinatorics

Published online by Cambridge University Press:  10 February 2015

JÓZSEF SOLYMOSI
JÓZSEF SOLYMOSI*
Affiliation:
Department of Mathematics, University of British Columbia, 1984 Mathematics Road, Vancouver, BC, V6T 1Z4, Canada (e-mail: solymosi@math.ubc.ca)
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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 such that if a quasigroup has order n ⩾ n0, then for every subset S of triples of the form (a, b, ab) with |S| ⩾ cn2, there is a seven-element subset of the quasigroup which spans at least four triples of S. In this paper we prove the conjecture for finite groups.

MSC classification

Primary: 05D05: Extremal set theory
Secondary: 05E15: Combinatorial aspects of groups and algebras
Type
Paper
Information
Combinatorics, Probability and Computing , Volume 24 , Special Issue 4: Oberwolfach Special Issue Part 1 , July 2015 , pp. 680 - 686
Copyright
Copyright © Cambridge University Press 2015 

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