منابع مشابه
On divisibility in definable groups
Let M be an o–minimal expansion of a real closed field. It is known that a definably connected abelian group is divisible. In this note, we show that a definably compact definably connected group is divisible.
متن کاملnon-divisibility for abelian groups
Throughout all groups are abelian. We say a group G is n-divisible if nG = G. If G has no non-zero n-divisible subgroups for all n>1 then we say that G is absolutely non-divisible. In the study of class C consisting all absolutely non-divisible groups such as G, we come across the sub groups T_p(G) = the sum of all p-divisible subgroups and rad_p(G) = the intersection of all p^nG. The proper...
متن کاملDefinable Representations of Definable C Groups
Let G be a compact affine definable C group and let r be∞ or ω. We prove that the representative definable C functions on G is dense in the space of continuous functions on G. Moreover we compare the category of compact affine definable C groups D with that of compact real algebraic groups A.
متن کاملDefinable Maximal Cofinitary Groups
Using countable support iteration of S-proper posets, for some appropriate stationary set S, we obtain a generic extension of the constructible universe, in which b = c = א2 and there is a maximal cofinitary group with a Π2-definable set of generators.
متن کاملOn the Euler characteristic of definable groups
We show that in an arbitrary o-minimal structure the following are equivalent: (i) conjugates of a definable subgroup of a definably connected, definably compact definable group cover the group if the o-minimal Euler characteristic of the quotient is non zero; (ii) every infinite, definably connected, definably compact definable group has a non trivial torsion point. ∗The author was supported b...
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ژورنال
عنوان ژورنال: Fundamenta Mathematicae
سال: 2009
ISSN: 0016-2736,1730-6329
DOI: 10.4064/fm202-3-6