TY - JOUR

T1 - Separability of Schur Rings over Abelian p-Groups

AU - Ryabov, G. K.

PY - 2018/5/19

Y1 - 2018/5/19

N2 - 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|.

AB - 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|.

KW - Cayley graph isomorphism problem

KW - Cayley graphs

KW - Cayley schemes

KW - permutation groups

KW - Schur rings

UR - http://www.scopus.com/inward/record.url?scp=85047108184&partnerID=8YFLogxK

U2 - 10.1007/s10469-018-9478-5

DO - 10.1007/s10469-018-9478-5

M3 - Article

AN - SCOPUS:85047108184

VL - 57

SP - 49

EP - 68

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 1

ER -