Geodesic
Separability of Schur rings over Abelian $p$-groups
Algebra i logika, Tome 57 (2018) no. 1, pp. 73-101

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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 $C_n$ be the cyclic group of order $n$. It is proved that all $S$-rings over groups $D=C_p\times C_{p^k}$, where $p\in\{2,3\}$ and $k\ge1$, 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 $|D|$.
Keywords: Cayley graphs, Cayley graph isomorphism problem, Cayley schemes, Schur rings, permutation groups. 
@article{AL_2018_57_1_a4,
     author = {G. K. Ryabov},
     title = {Separability of {Schur} rings over {Abelian} $p$-groups},
     journal = {Algebra i logika},
     pages = {73--101},
     publisher = {mathdoc},
     volume = {57},
     number = {1},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2018_57_1_a4/}
}
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G. K. Ryabov. Separability of Schur rings over Abelian $p$-groups. Algebra i logika, Tome 57 (2018) no. 1, pp. 73-101. http://geodesic.mathdoc.fr/item/AL_2018_57_1_a4/