Реферат: 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. © 2019, Springer Science+Business Media, LLC, part of Springer Nature.

Библиографическая ссылка: Romanovskii N.S.
Divisible Rigid Groups. III. Homogeneity and Quantifier Elimination
Algebra and Logic. 2019. V.57. N6. P.478-489. DOI: 10.1007/s10469-019-09518-2 WOS Scopus OpenAlex

Идентификаторы БД:

Web of science:	WOS:000463584500006
Scopus:	2-s2.0-85063814703
OpenAlex:	W2924409976

Цитирование в БД:

БД	Цитирований
Scopus	6
OpenAlex	6
Web of science	6

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