TY - JOUR

T1 - Divisible Rigid Groups. Morley Rank

AU - Romanovskii, N. S.

N1 - Funding Information: This work was supported by the National Natural Science Foundation of China (No. 81971406, 81871185), The 111 Project (Yuwaizhuan (2016)32), Chongqing Science & Technology Commission (cstc2021jcyj-msxmX0213), Chongqing Municipal Education Commission (KJZD-K202100407), Chongqing Health Commission and Chongqing Science & Technology Commission (2021MSXM121, 2020MSXM101). Publisher Copyright: © 2022, The Author(s), under exclusive licence to Springer Nature Switzerland AG.

PY - 2022/7

Y1 - 2022/7

N2 - Let G be a countable saturated model of the theory Im of divisible m-rigid groups. Fix the splitting G1G2..Gm of a group G into a semidirect product of Abelian groups. With each tuple (n1,.. , nm) of nonnegative integers we associate an ordinal α = ωm−1nm+.. + ωn2 + n1 and denote by G(α) the set G1n1×G2n2×…×Gmnm, which is definable over G in Gn1+…+nm. Then the Morley rank of G(α) with respect to G is equal to α. This implies that RM (G) = ωm−1 + ωm−2 +.. + 1.

AB - Let G be a countable saturated model of the theory Im of divisible m-rigid groups. Fix the splitting G1G2..Gm of a group G into a semidirect product of Abelian groups. With each tuple (n1,.. , nm) of nonnegative integers we associate an ordinal α = ωm−1nm+.. + ωn2 + n1 and denote by G(α) the set G1n1×G2n2×…×Gmnm, which is definable over G in Gn1+…+nm. Then the Morley rank of G(α) with respect to G is equal to α. This implies that RM (G) = ωm−1 + ωm−2 +.. + 1.

KW - divisible m-rigid group

KW - Morley rank

UR - http://www.scopus.com/inward/record.url?scp=85144067421&partnerID=8YFLogxK

UR - https://www.mendeley.com/catalogue/74e2c3ce-a844-3b13-9213-6c3f0abc7e6e/

U2 - 10.1007/s10469-022-09689-5

DO - 10.1007/s10469-022-09689-5

M3 - Article

AN - SCOPUS:85144067421

VL - 61

SP - 207

EP - 224

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 3

ER -