TY - JOUR

T1 - On separable abelian p-groups

AU - Ryabov, Grigory

PY - 2019/1/1

Y1 - 2019/1/1

N2 - An S-ring (a Schur ring) is said to be separable with respect to a class of groups K if every algebraic isomorphism from the S-ring in question to an S-ring over a group from K is induced by a combinatorial isomorphism. A finite group is said to be separable with respect to K if every S-ring over this group is separable with respect to K. We provide a complete classification of abelian p-groups separable with respect to the class of abelian groups.

AB - An S-ring (a Schur ring) is said to be separable with respect to a class of groups K if every algebraic isomorphism from the S-ring in question to an S-ring over a group from K is induced by a combinatorial isomorphism. A finite group is said to be separable with respect to K if every S-ring over this group is separable with respect to K. We provide a complete classification of abelian p-groups separable with respect to the class of abelian groups.

KW - Isomorphisms

KW - P-groups

KW - Schur rings

UR - http://www.scopus.com/inward/record.url?scp=85076237421&partnerID=8YFLogxK

U2 - 10.26493/1855-3974.1892.78f

DO - 10.26493/1855-3974.1892.78f

M3 - Article

AN - SCOPUS:85076237421

VL - 17

SP - 467

EP - 479

JO - Ars Mathematica Contemporanea

JF - Ars Mathematica Contemporanea

SN - 1855-3966

IS - 2

ER -