Related papers: Fields definable in the free group
We address the problem of finding necessary and sufficient conditions for an arbitrary group, not necessarily finite, to admit a faithful irreducible representation over an arbitrary field.
We show the existence of noncommutative random variables with finite free entropy but which do not generate a free group factor.
We prove various finite de Finetti theorems for non-commutative distributions which are invariant under the free easy quantum group actions. This complements the free de Finetti theorems by Banica, Curran and Speicher, which mostly focus on…
We continue our earlier study of finite dimensional definable groups in models of the the model companion of an o-minimal L-theory T expanded by a generic derivation as in [F-K]. We generalize Buium's notion of an algebraic D-group to…
We present a new proof that the statement 'every subgroup of a free group is free' implies the Axiom of Choice for finite sets.
We prove that certain fields have the property that their absolute Galois groups are free as profinite groups: the function field of a real curve with no real points; the maximal abelian extension of a 2-variable Laurent series field over a…
Let ${\bf F}$ be a field of characteristic zero. It is proved that for any finitely generated linear group $\Gamma<\mathsf{GL}_n({\bf F})$, every unipotent-free abelian subgroup of $\Gamma$ is separable.
We prove that every finite abelian group G occurs as a subgroup of the class group of infinitely many real cyclotomic fields.
In this paper we completely characterize solvable real Lie groups definable in o-minimal expansions of the real field.
In this paper we propose an algebraic formulation of group field theory and consider non-Fock representations based on coherent states. We show that we can construct representations with infinite number of degrees of freedom on compact base…
We consider random fields that can be represented as integrals of deterministic functions with respect to infinitely divisible random measures and show that these random fields are infinitely divisible.
A group is $\textit{finitely axiomatizable}$ (FA) in a class $\mathcal{C}$ if it can be determined up to isomorphism within $\mathcal{C}$ by a sentence in the first-order language of group theory. We show that profinite groups of various…
We determine all groups definable in Presburger arithmetic, up to a finite index subgroup.
We exhibit a theory where definable types lack the amalgamation property.
We study finite-dimensional groups definable in models of the theory of real closed fields with a generic derivation (also known as CODF). We prove that any such group definably embeds in a semialgebraic group. We extend the results to…
In this paper we study the relation between the category of real Lie groups and that of groups definable in o-minimal expansions of the real field, which we will refer to as ``definable groups''. With this terminology, it is known…
We investigate effective properties of uncountable free abelian groups. We show that identifying free abelian groups and constructing bases for such groups is often computationally hard, depending on the cardinality. For example, we show,…
Motivated by examples in infinite group theory, we classify the finite groups whose subgroups can never be decomposed as direct products.
In this article we classify all $L_9$-free finite groups.
We look for a deep connection between mathematics and physics. Our approach is to propose a set theory T which leads to a concise mathematical description of physical fields and to a finite unit of action. The concept of "definability" of…