Structure of k-Closures of Finite Nilpotent Permutation Groups

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Abstract

Let G be a permutation group of a set Ω and k be a positive integer. The k-closure of G is the greatest (w.r.t. inclusion) subgroup G(k) in Sym(Ω) which has the same orbits as has G under the componentwise action on the set Ωk. It is proved that the k-closure of a finite nilpotent group coincides with the direct product of k-closures of all of its Sylow subgroups.

Original languageEnglish
Pages (from-to)154-159
Number of pages6
JournalAlgebra and Logic
Volume60
Issue number2
DOIs
Publication statusPublished - May 2021

Keywords

  • finite nilpotent group
  • k-closure
  • Sylow subgroup

OECD FOS+WOS

  • 1.01 MATHEMATICS

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