A Schur ring (an S-ring) is said to be separable if each of its algebraic isomorphisms is induced by an isomorphism. Let C n be the cyclic group of order n. It is proved that all S-rings over groups \( D={C}_p\times {C}_{p^k} \), 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|.
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Supported by RFBR, project No. 17-51-53007.
Translated from Algebra i Logika, Vol. 57, No. 1, pp. 73-101, January-February, 2018.
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Ryabov, G.K. Separability of Schur Rings over Abelian p-Groups. Algebra Logic 57, 49–68 (2018). https://doi.org/10.1007/s10469-018-9478-5
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DOI: https://doi.org/10.1007/s10469-018-9478-5