{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:44:01Z","timestamp":1753893841256,"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>Given $k\\in \\mathbb{N}$ and a finite group $G$, it is shown that $G$ is isomorphic to a subgroup of the group of symmetries of some $n$-cube in such a way that $G$ acts freely on the set of  $k$-faces, if and only if, $\\gcd(k, |G|)=2^s$ for some non-negative integer $s$.  The proof of this result is existential but does give some ideas on what $n$ could be.<\/jats:p>","DOI":"10.37236\/683","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T03:41:19Z","timestamp":1578714079000},"source":"Crossref","is-referenced-by-count":0,"title":["Finite Groups of Derangements on the $n$-Cube II"],"prefix":"10.37236","volume":"18","author":[{"given":"Larry","family":"Cusick","sequence":"first","affiliation":[]},{"given":"Oscar","family":"Vega","sequence":"additional","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2011,10,3]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p196\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v18i1p196\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T23:01:14Z","timestamp":1579302074000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v18i1p196"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2011,10,3]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2011,1,5]]}},"URL":"https:\/\/doi.org\/10.37236\/683","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2011,10,3]]},"article-number":"P196"}}