identifying long cycles in finite alternating and symmetric groups acting on subsets
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ID: 254354
2015
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Abstract
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 $\Lambda$.
| Reference Key |
linton2015journalidentifying
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|---|---|
| Authors | ;Steve Linton;Alice C. Niemeyer;Cheryl Praeger |
| Journal | Plant disease |
| Year | 2015 |
| DOI |
10.13069/jacodesmath.28239
|
| URL | |
| Keywords | Keywords not found |
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