TY - JOUR
T1 - Generic Types and Generic Elements in Divisible Rigid Groups
AU - Myasnikov, A. G.
AU - Romanovskii, N. S.
N1 - Publisher Copyright:
© 2024, Siberian Fund of Algebra and Logic.
PY - 2023/3
Y1 - 2023/3
N2 - A group G is said to be m-rigid if it contains a normal series of the form G = G 1 > G 2 >.. > Gm > Gm+1 = 1, whose quotients Gi/Gi+1 are Abelian and, treated as (right) ℤ[G/Gi]-modules, are torsion-free. A rigid group G is said to be divisible if elements of the quotient ρi(G)/ρi+1(G) are divisible by nonzero elements of the ring ℤ[G/ρi(G)]. Previously, it was proved that the theory of divisible m-rigid groups is complete and ω-stable. In the present paper, we give an algebraic description of elements and types that are generic over a divisible m-rigid group G.
AB - A group G is said to be m-rigid if it contains a normal series of the form G = G 1 > G 2 >.. > Gm > Gm+1 = 1, whose quotients Gi/Gi+1 are Abelian and, treated as (right) ℤ[G/Gi]-modules, are torsion-free. A rigid group G is said to be divisible if elements of the quotient ρi(G)/ρi+1(G) are divisible by nonzero elements of the ring ℤ[G/ρi(G)]. Previously, it was proved that the theory of divisible m-rigid groups is complete and ω-stable. In the present paper, we give an algebraic description of elements and types that are generic over a divisible m-rigid group G.
KW - divisible m-rigid group
KW - generic element
KW - generic type
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U2 - 10.1007/s10469-023-09726-x
DO - 10.1007/s10469-023-09726-x
M3 - Article
AN - SCOPUS:85181234629
SN - 0002-5232
VL - 62
SP - 72
EP - 79
JO - Algebra and Logic
JF - Algebra and Logic
IS - 1
ER -