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Divisible Rigid Groups. III. Homogeneity and Quantifier Elimination. / Romanovskii, N. S.

в: Algebra and Logic, Том 57, № 6, 15.01.2019, стр. 478-489.

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Romanovskii NS. Divisible Rigid Groups. III. Homogeneity and Quantifier Elimination. Algebra and Logic. 2019 янв. 15;57(6):478-489. doi: 10.1007/s10469-019-09518-2

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Romanovskii, N. S. / Divisible Rigid Groups. III. Homogeneity and Quantifier Elimination. в: Algebra and Logic. 2019 ; Том 57, № 6. стр. 478-489.

BibTeX

@article{c54aa5ae0abf416f8a3bc8934dd89293,
title = "Divisible Rigid Groups. III. Homogeneity and Quantifier Elimination",
abstract = " A group G is said to be rigid if it contains a normal series G = G 1 > G 2 >.. > G m > G m+1 = 1, whose quotients G i /G i+1 are Abelian and, treated as right ℤ[G/G i ]-modules, are torsion-free. A rigid group G is divisible if elements of the quotient G i /G i+1 are divisible by nonzero elements of the ring ℤ[G/G i ]. Every rigid group is embedded in a divisible one. Our main result is the theorem which reads as follows. Let G be a divisible rigid group. Then the coincidence of ∃-types of same-length tuples of elements of the group G implies that these tuples are conjugate via an automorphism of G. As corollaries we state that divisible rigid groups are strongly ℵ 0 -homogeneous and that the theory of divisible m-rigid groups admits quantifier elimination down to a Boolean combination of ∃-formulas. ",
keywords = "divisible group, quantifier elimination, rigid group, strongly ℵ -homogeneous group, strongly (0)-homogeneous group",
author = "Romanovskii, {N. S.}",
year = "2019",
month = jan,
day = "15",
doi = "10.1007/s10469-019-09518-2",
language = "English",
volume = "57",
pages = "478--489",
journal = "Algebra and Logic",
issn = "0002-5232",
publisher = "Springer US",
number = "6",

}

RIS

TY - JOUR

T1 - Divisible Rigid Groups. III. Homogeneity and Quantifier Elimination

AU - Romanovskii, N. S.

PY - 2019/1/15

Y1 - 2019/1/15

N2 - A group G is said to be rigid if it contains a normal series G = G 1 > G 2 >.. > G m > G m+1 = 1, whose quotients G i /G i+1 are Abelian and, treated as right ℤ[G/G i ]-modules, are torsion-free. A rigid group G is divisible if elements of the quotient G i /G i+1 are divisible by nonzero elements of the ring ℤ[G/G i ]. Every rigid group is embedded in a divisible one. Our main result is the theorem which reads as follows. Let G be a divisible rigid group. Then the coincidence of ∃-types of same-length tuples of elements of the group G implies that these tuples are conjugate via an automorphism of G. As corollaries we state that divisible rigid groups are strongly ℵ 0 -homogeneous and that the theory of divisible m-rigid groups admits quantifier elimination down to a Boolean combination of ∃-formulas.

AB - A group G is said to be rigid if it contains a normal series G = G 1 > G 2 >.. > G m > G m+1 = 1, whose quotients G i /G i+1 are Abelian and, treated as right ℤ[G/G i ]-modules, are torsion-free. A rigid group G is divisible if elements of the quotient G i /G i+1 are divisible by nonzero elements of the ring ℤ[G/G i ]. Every rigid group is embedded in a divisible one. Our main result is the theorem which reads as follows. Let G be a divisible rigid group. Then the coincidence of ∃-types of same-length tuples of elements of the group G implies that these tuples are conjugate via an automorphism of G. As corollaries we state that divisible rigid groups are strongly ℵ 0 -homogeneous and that the theory of divisible m-rigid groups admits quantifier elimination down to a Boolean combination of ∃-formulas.

KW - divisible group

KW - quantifier elimination

KW - rigid group

KW - strongly ℵ -homogeneous group

KW - strongly (0)-homogeneous group

UR - http://www.scopus.com/inward/record.url?scp=85063814703&partnerID=8YFLogxK

U2 - 10.1007/s10469-019-09518-2

DO - 10.1007/s10469-019-09518-2

M3 - Article

AN - SCOPUS:85063814703

VL - 57

SP - 478

EP - 489

JO - Algebra and Logic

JF - Algebra and Logic

SN - 0002-5232

IS - 6

ER -

ID: 19278035