Research output: Contribution to journal › Article › peer-review
Separability of Schur Rings over Abelian p-Groups. / Ryabov, G. K.
In: Algebra and Logic, Vol. 57, No. 1, 19.05.2018, p. 49-68.Research output: Contribution to journal › Article › peer-review
}
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 -
ID: 13488460