Separability of Schur Rings over Abelian p-Groups

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 × C p k , where p ∈ {2, 3} and k ≥ 1, are separable with respect to a class of S -rings ov...

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Bibliographic Details
Published in:Algebra and logic 2018-03, Vol.57 (1), p.49-68
Main Author: Ryabov, G. K.
Format: Article
Language:English
Subjects:
Algebra
Isomorphism
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Rings (mathematics)
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Summary: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 × 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 |.
ISSN:0002-5232
1573-8302
DOI:10.1007/s10469-018-9478-5