Disjoint direct product decompositions of permutation groups

Mun See Chang*, Christopher Anthony Jefferson

*Corresponding author for this work

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Let H ≤ Sn be an intransitive group with orbits Ω1, Ω2, ... , Ωk. Then certainly H is a subdirect product of the direct product of its projections on each orbit, H|Ω1 x H|Ω2 x ... x H|Ωk. Here we provide a polynomial time algorithm for computing the finest partition P of the H-orbits such that H = Πc∈P H|c and we demonstrate its usefulness in some applications.
Original languageEnglish
Pages (from-to)1-16
JournalJournal of Symbolic Computation
Early online date29 Apr 2021
Publication statusPublished - Jan 2022


  • Permutation group
  • Computation
  • Direct product
  • Subdirect product
  • Decomposition
  • Computer algebra system


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