{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T14:17:47Z","timestamp":1775053067307,"version":"3.50.1"},"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 acting faithfully on a set $X$.  The distinguishing number of the action of $G$ on $X$, denoted $D_G(X)$, is the smallest number of colors such that there exists a coloring of $X$ where no nontrivial group element induces a color-preserving permutation of $X$.  In this paper, we show that if $G$ is nilpotent of class $c$ or supersolvable of length $c$ then $G$ always acts with distinguishing number at most $c+1$.  We obtain that all metacyclic groups act with distinguishing number at most 3; these include all groups of squarefree order.  We also prove that the distinguishing number of the action of the general linear group $GL_n(K)$ over a field $K$ on the vector space $K^n$ is 2 if $K$ has at least $n+1$ elements.<\/jats:p>","DOI":"10.37236\/1096","type":"journal-article","created":{"date-parts":[[2020,1,11]],"date-time":"2020-01-11T04:59:05Z","timestamp":1578718745000},"source":"Crossref","is-referenced-by-count":12,"title":["The Maximum Distinguishing Number of a Group"],"prefix":"10.37236","volume":"13","author":[{"given":"Melody","family":"Chan","sequence":"first","affiliation":[]}],"member":"23455","published-online":{"date-parts":[[2006,8,7]]},"container-title":["The Electronic Journal of Combinatorics"],"original-title":[],"link":[{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r70\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/download\/v13i1r70\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,1,18]],"date-time":"2020-01-18T04:09:55Z","timestamp":1579320595000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.combinatorics.org\/ojs\/index.php\/eljc\/article\/view\/v13i1r70"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2006,8,7]]},"references-count":0,"journal-issue":{"issue":"1","published-online":{"date-parts":[[2006,1,7]]}},"URL":"https:\/\/doi.org\/10.37236\/1096","relation":{},"ISSN":["1077-8926"],"issn-type":[{"value":"1077-8926","type":"electronic"}],"subject":[],"published":{"date-parts":[[2006,8,7]]},"article-number":"R70"}}