most recent 30 from http://mathoverflow.net 2013-05-25T09:50:15Z http://mathoverflow.net/feeds/question/103009 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/103009/does-probability-of-a-derangement-go-up-under-passing-to-subgroups David Speyer 2012-07-24T15:12:29Z 2012-07-24T15:54:53Z

<p>This is prompted by my attempts to work on <a href="http://mathoverflow.net/questions/102751/a-mixing-property-for-finite-fields-of-characteristic-2/" rel="nofollow">this question</a>. Let $H \subset G \subseteq S_d$ be transitive permutation groups. Recall that an element of $S_d$ is called a derangement if it has no fixed points.</p> <blockquote> <p>Is the proportion of derangements in $H$ always greater than in $G$?</p> </blockquote> <p>If $H$ doesn't have to be transitive, then the answer is "no"; just let $H$ be trivial. But a quick sampling of examples with $G$ and $H$ both transitive doesn't turn up any counterexamples.</p> <p><b>UPDATE</b> Never mind. $A_4$ inside $S_4$, the probability of a derangement goes down from $3/8$ to $1/4$.</p>