Separability of Schur Rings over Abelian p-Groups

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A Schur ring (an S-ring) is said to be separable if each of its algebraic isomorphisms is induced by an isomorphism. Let Cn be the cyclic group of order n. It is proved that all S-rings over groups (Formula presented.), where p ∈ {2, 3} and k ≥ 1, are separable with respect to a class of S-rings over Abelian groups. From this statement, we deduce that a given Cayley graph over D and a given Cayley graph over an arbitrary Abelian group can be checked for isomorphism in polynomial time with respect to |D|.

Original languageEnglish
Pages (from-to)49-68
Number of pages20
JournalAlgebra and Logic
Issue number1
Publication statusAccepted/In press - 19 May 2018


  • Cayley graph isomorphism problem
  • Cayley graphs
  • Cayley schemes
  • permutation groups
  • Schur rings


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