Related papers: Groups definable in Presburger arithmetic
This paper is devoted to understand groups definable in Presburger arithmetic. We prove the following theorems: Theorem 1. Every group definable in a model of Presburger Arithmetic is abelian-by-finite. Theorem 2. Every bounded group…
We entirely classify definable sets up to definable bijections in $\mathbb{Z}$-groups, where the language is the one of ordered abelian groups. From this, we deduce, among others, a classification of definable families of bounded definable…
A complete list of one dimensional groups definable in the p-adic numbers is given, up to a finite index subroup and a quotient by a finite subgroup.
We present a description of rigid models of Presburger arithmetic (i.e., Z-groups). In particular, we show that Presburger arithmetic has rigid models of all infinite cardinalities up to the continuum, but no larger.
We classify the finitely generated prosupersolvable groups that satisfy Schreier's formula for the number of generators of open subgroups.
The main goal of this paper is to apply the arithmetic method developed in our previous paper \cite{13} to determine the number of some types of subgroups of finite abelian groups.
We give a complete list of the one-dimensional groups definable in algebraically closed valued fields and i the pseudo-local fields, up to a finite index subgroup and a quotient by a finite subgroup.
We define the notion of accessibility for a pro-$p$ group. We prove that finitely generated pro-$p$ groups are accessible given a bound on the size of their finite subgroups. We then construct a finitely generated inaccessible pro-$p$…
We define a notion of an arithmetic set in an arbitrary countable group and study properties of these sets in the cases of Abelian groups and non-abelian free groups.
We survey recent work ranging around the question in how far a group, or a property of a group, is determined by the set of finite quotient groups. Our focus lies on $S$-arithmetic groups, branch groups, and their relatives.
We show pro-definability of spaces of definable types in various classical complete first order theories, including complete o-minimal theories, Presburger arithmetic, $p$-adically closed fields, real closed and algebraically closed valued…
We determine the finite groups whose real irreducible representations have different degrees.
In this work we carry out a complete group classification of Burgers' equations.
The principle result of this article is the determination of the possible finite subgroups of arithmetic lattices in U(2,1).
For every group of order at most 14 we determine the values taken by its group determinant when its variables are integers.
We determine all finite subgroups of simple algebraic groups that have irreducible centralizers - that is, centralizers whose connected component does not lie in a parabolic subgroup.
We define a class of pre-ordered abelian groups that we call finite-by-Presburger groups, and prove that their theory is model-complete. We show that certain quotients of the multiplicative group of a local field of characteristic zero are…
We provide a family of group measure space II_1 factors for which all finite index subfactors can be explicitly listed. In particular, the set of all indices of irreducible subfactors can be computed. Concrete examples show that this index…
We prove that in an arbitrary o-minimal structure, every interpretable group is definably isomorphic to a definable one. We also prove that every definable group lives in a cartesian product of one-dimensional definable group-intervals (or…
We define precuspidal families in proper parabolic subgroups of a Weyl group and we show how to use them to index the irreducible representations of that Weyl group in terms of certain pairs of finite groups. Some additional material is…