Identifying long cycles in finite alternating and symmetric groups acting on subsets
Abstract
Let H be a permutation group on a set Λ, which is permutationally isomorphic to a finite alternating or symmetric group An or Sn acting on the k-element subsets of points from {1, . . . , 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 ϕ, such as those whose image under ϕ is an n-cycle or (n − 1)-cycle, can be recognised with high probability by the lengths of just four of their cycles in Λ.
Citation
Linton , S A , Niemeyer , A C & Praeger , C E 2015 , ' Identifying long cycles in finite alternating and symmetric groups acting on subsets ' , Journal of Algebra Combinatorics Discrete Structures and Applications , vol. 2 , no. 2 , pp. 117-149 . https://doi.org/10.13069/jacodesmath.28239
Publication
Journal of Algebra Combinatorics Discrete Structures and Applications
Status
Peer reviewed
ISSN
2148-838XType
Journal article
Collections
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