%0 Journal Article
%T Identifying long cycles in finite alternating and symmetric groups acting on subsets
%A Steve Linton
%A Alice C. Niemeyer
%A Cheryl E. Praeger
%J Mathematics
%D 2012
%I arXiv
%X Let $H$ be a permutation group on a set $\Lambda$, which is permutationally isomorphic to a finite alternating or symmetric group $A_n$ or $S_n$ acting on the $k$-element subsets of points from $\{1,\ldots,n\}$, for some arbitrary but fixed $k$. Suppose moreover that no isomorphism with this action is known. We show that key elements of $H$ needed to construct such an isomorphism $\varphi$, such as those whose image under $\varphi$ is an $n$-cycle or $(n-1)$-cycle, can be recognised with high probability by the lengths of just four of their cycles in $\Lambda$.
%U http://arxiv.org/abs/1205.6586v3