{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,28]],"date-time":"2025-09-28T12:50:00Z","timestamp":1759063800249},"reference-count":18,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2015,2,10]],"date-time":"2015-02-10T00:00:00Z","timestamp":1423526400000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Combinator. Probab. Comp."],"published-print":{"date-parts":[[2015,7]]},"abstract":"<jats:p>The first open case of the Brown\u2013Erd\u0151s\u2013S\u00f3s conjecture is equivalent to the following: for every <jats:italic>c<\/jats:italic> &gt; 0, there is a threshold <jats:italic>n<\/jats:italic><jats:sub>0<\/jats:sub> such that if a quasigroup has order <jats:italic>n<\/jats:italic> \u2a7e <jats:italic>n<\/jats:italic><jats:sub>0<\/jats:sub>, then for every subset <jats:italic>S<\/jats:italic> of triples of the form (<jats:italic>a, b, ab<\/jats:italic>) with |<jats:italic>S<\/jats:italic>| \u2a7e <jats:italic>cn<\/jats:italic><jats:sup>2<\/jats:sup>, there is a seven-element subset of the quasigroup which spans at least four triples of <jats:italic>S<\/jats:italic>. In this paper we prove the conjecture for finite groups.<\/jats:p>","DOI":"10.1017\/s0963548314000856","type":"journal-article","created":{"date-parts":[[2015,2,10]],"date-time":"2015-02-10T14:24:24Z","timestamp":1423578264000},"page":"680-686","source":"Crossref","is-referenced-by-count":11,"title":["The (7, 4)-Conjecture in Finite Groups"],"prefix":"10.1017","volume":"24","author":[{"given":"J\u00d3ZSEF","family":"SOLYMOSI","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2015,2,10]]},"reference":[{"key":"S0963548314000856_ref15","first-page":"939","volume-title":"Combinatorics: Proc. 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