TY - JOUR

T1 - Divisible Rigid Groups. IV. Definable Subgroups

AU - Romanovskii, N. S.

N1 - Funding Information: N. S. Romanovskii is supported by Russian Science Foundation, project No. 19-11-00039. Publisher Copyright: © 2020, Springer Science+Business Media, LLC, part of Springer Nature. Copyright: Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2020/7

Y1 - 2020/7

N2 - A group G is said to be rigid if it contains a normal series G = G1 > G2 > … > Gm > Gm+1 = 1, whose quotients Gi/Gi+1 are Abelian and, when treated as right ℤ[G/Gi]-modules, are torsion-free. A rigid group G is divisible if elements of the quotient Gi/Gi+1 are divisible by nonzero elements of the ring ℤ[G/Gi]. We describe subgroups of a divisible rigid group which are definable in the signature of the theory of groups without parameters and with parameters.

AB - A group G is said to be rigid if it contains a normal series G = G1 > G2 > … > Gm > Gm+1 = 1, whose quotients Gi/Gi+1 are Abelian and, when treated as right ℤ[G/Gi]-modules, are torsion-free. A rigid group G is divisible if elements of the quotient Gi/Gi+1 are divisible by nonzero elements of the ring ℤ[G/Gi]. We describe subgroups of a divisible rigid group which are definable in the signature of the theory of groups without parameters and with parameters.

KW - definable subgroup

KW - divisible group

KW - rigid group

UR - http://www.scopus.com/inward/record.url?scp=85094635251&partnerID=8YFLogxK

U2 - 10.1007/s10469-020-09596-7

DO - 10.1007/s10469-020-09596-7

M3 - Article

AN - SCOPUS:85094635251

VL - 59

SP - 237

EP - 252

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 3

ER -