{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:43:14Z","timestamp":1753893794103,"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 show that an action of SL$(2,p)$, $p\\ge 7$ an odd prime such that $4\\mathrel{\\not|}(p-1)$, has exactly two orbital digraphs $\\Gamma_1$, $\\Gamma_2$, such that Aut$(\\Gamma_i)$ admits a complete block system ${\\cal B}$ of $p+1$ blocks of size $2$, $i = 1,2$, with the following properties:  the action of Aut$(\\Gamma_i)$ on the blocks of ${\\cal B}$ is nonsolvable, doubly-transitive, but not a symmetric group, and the subgroup of Aut$(\\Gamma_i)$ that fixes each block of ${\\cal B}$ set-wise is semiregular of order $2$.  If $p = 2^k - 1 &gt; 7$ is a Mersenne prime, these digraphs are also Cayley digraphs of the generalized quaternion group of order $2^{k+1}$.  In this case, these digraphs are non-normal Cayley digraphs of the generalized quaternion group of order $2^{k+1}$.<\/jats:p>","DOI":"10.37236\/1724","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T07:03:33Z","timestamp":1578639813000},"source":"Crossref","is-referenced-by-count":1,"title":["Some Non-Normal Cayley Digraphs of the Generalized Quaternion Group of Certain Orders"],"prefix":"10.37236","volume":"10","author":[{"given":"Edward","family":"Dobson","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2003,9,8]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r31\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v10i1r31\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T05:07:10Z","timestamp":1579324030000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v10i1r31"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2003,9,8]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2003,1,6]]}},"URL":"https:\/\/doi.org\/10.37236\/1724","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2003,9,8]]},"article-number":"R31"}}