{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,9,25]],"date-time":"2025-09-25T18:10:33Z","timestamp":1758823833448,"version":"3.41.2"},"reference-count":0,"publisher":"The Electronic Journal of Combinatorics","issue":"4","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Electron. J. Combin."],"abstract":"<jats:p>We consider the action of the $2$-dimensional projective general linear group $PGL(2,q)$ on the projective line $PG(1,q)$. A subset $S$ of $PGL(2,q)$ is said to be an intersecting family if for every $g_1,g_2 \\in S$, there exists $\\alpha \\in PG(1,q)$ such that $\\alpha^{g_1}= \\alpha^{g_2}$. It was proved by Meagher and Spiga that the intersecting families of maximum size in $PGL(2,q)$ are precisely the cosets of point stabilizers. We prove that if an intersecting family $S \\subset PGL(2,q)$ has size close to the maximum then it must be \"close\" in structure to a coset of a point stabilizer. This phenomenon is known as stability. We use this stability result proved here to show that if the size of $S$ is close enough to the maximum then $S$ must be contained in a coset of a point stabilizer.<\/jats:p>","DOI":"10.37236\/5401","type":"journal-article","created":{"date-parts":[[2020,1,10]],"date-time":"2020-01-10T22:18:30Z","timestamp":1578694710000},"source":"Crossref","is-referenced-by-count":3,"title":["Stability for Intersecting Families in PGL(2,q)"],"prefix":"10.37236","volume":"22","author":[{"given":"Rafael","family":"Plaza","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2015,12,23]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p41\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v22i4p41\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,17]],"date-time":"2020-01-17T05:37:38Z","timestamp":1579239458000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v22i4p41"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2015,12,23]]},"references-count":0,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2015,10,16]]}},"URL":"https:\/\/doi.org\/10.37236\/5401","relation":{},"ISSN":["1077-8926"],"issn-type":[{"type":"electronic","value":"1077-8926"}],"subject":[],"published":{"date-parts":[[2015,12,23]]},"article-number":"P4.41"}}