{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:59Z","timestamp":1753893839525,"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>We resolve the existence problem of $(96,20,4)$ difference sets in 211 of 231 groups of order $96$.  If $G$ is a group of order $96$ with normal subgroups of orders $3$ and $4$ then by first computing $32$- and $24$-factor images of a hypothetical $(96,20,4)$ difference set in $G$ we are able to either construct a difference set or show a difference set does not exist. Of the 231 groups of order 96, 90 groups admit $(96,20,4)$ difference sets and $121$ do not.  The ninety groups with difference sets provide many genuinely nonabelian difference sets.  Seven of these groups have exponent 24. These difference sets provide at least $37$ nonisomorphic symmetric $(96,20,4)$ designs.<\/jats:p>","DOI":"10.37236\/927","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:52:35Z","timestamp":1578718355000},"source":"Crossref","is-referenced-by-count":1,"title":["Nonabelian Groups with $(96,20,4)$ Difference Sets"],"prefix":"10.37236","volume":"14","author":[{"given":"Omar A.","family":"AbuGhneim","sequence":"first","affiliation":[]},{"given":"Ken W.","family":"Smith","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2007,1,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r8\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v14i1r8\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:05:12Z","timestamp":1579320312000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v14i1r8"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2007,1,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2007,1,3]]}},"URL":"https:\/\/doi.org\/10.37236\/927","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2007,1,3]]},"article-number":"R8"}}