{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:42:53Z","timestamp":1753893773512,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"1","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>Let $G$ be a group and $S$ a non-empty subset of $G$. If $ab \\notin S$ for any $a, b \\in S$, then $S$ is called sum-free. We show that if $S$ is maximal by inclusion and no proper subset generates $\\langle S\\rangle$ then $|S|\\leq 2$. We determine all groups with a maximal (by inclusion) sum-free set of size at most 2 and all of size 3 where there exists $a \\in S$ such that $a \\notin \\langle S \\setminus \\{a\\}\\rangle$.<\/jats:p>","DOI":"10.37236\/148","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:31:42Z","timestamp":1578717102000},"source":"Crossref","is-referenced-by-count":7,"title":["Small Maximal Sum-Free Sets"],"prefix":"10.37236","volume":"16","author":[{"given":"Michael","family":"Giudici","sequence":"first","affiliation":[]},{"given":"Sarah","family":"Hart","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2009,5,11]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r59\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v16i1r59\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T02:55:30Z","timestamp":1579316130000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v16i1r59"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2009,5,11]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2009,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/148","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2009,5,11]]},"article-number":"R59"}}