-groups and pseudo-bad groups.
A locally commutative free group acting on the plane
The purpose of this paper is to prove the existence of a free subgroup of the group of all affine transformations on the plane with determinant 1 such that the action of the subgroup is locally commutative.
A note on generic subsets of definable groups
We generalize the theory of generic subsets of definably compact definable groups to arbitrary o-minimal structures. This theory is a crucial part of the solution to Pillay's conjecture connecting definably compact definable groups with Lie groups.
An elementary class extending abelian-by- groups, for infinite
We show that for no infinite group the class of abelian-by- groups is elementary, but, at least when is an infinite elementary abelian -group (with prime), the class of groups admitting a normal abelian subgroup whose quotient group is elementarily equivalent to is elementary.
Around Podewski's conjecture
A long-standing conjecture of Podewski states that every minimal field is algebraically closed. Known in positive characteristic, it remains wide open in characteristic zero. We reduce Podewski's conjecture to the (partially) ordered case, and we conjecture that such fields do not exist. We prove the conjecture in case the incomparability relation is transitive (the almost linear case). We also study minimal groups with a (partial) order, and give a complete classification of...
Cancellation of Abelian groups of finite rank modulo elementary equivalence.
Congruence relations on cone semigroups.
Die Struktur kartesischer Produkte ganzer Zahlen modulo kartesische Produkte ganzer Zahlen.
Elementary embeddings in torsion-free hyperbolic groups
We describe first-order logic elementary embeddings in a torsion-free hyperbolic group in terms of Sela’s hyperbolic towers. Thus, if embeds elementarily in a torsion free hyperbolic group , we show that the group can be obtained by successive amalgamations of groups of surfaces with boundary to a free product of with some free group and groups of closed surfaces. This gives as a corollary that an elementary subgroup of a finitely generated free group is a free factor. We also consider the...
Erratum to: “Elementary embeddings in torsion-free hyperbolic groups”
Existency-Closed Groups in X_1 with Special Properties
Finite images and elementary equivalence of completely regular inverse semigroups.
First Order Classes of Groups Having no Groups With a Given Property
Groupes nilpotents existentiellement clos de classe fixée
Inert subgroups of uncountable locally finite groups
Let be an uncountable universal locally finite group. We study subgroups such that for every , .
Infinitary stationary logic and abelian groups
Interpreting number theory in nilpotent groups.
Kleinian groups (a survey)
Limits of relatively hyperbolic groups and Lyndon’s completions
We describe finitely generated groups universally equivalent (with constants from in the language) to a given torsion-free relatively hyperbolic group with free abelian parabolics. It turns out that, as in the free group case, the group embeds into the Lyndon’s completion of the group , or, equivalently, embeds into a group obtained from by finitely many extensions of centralizers. Conversely, every subgroup of containing is universally equivalent to . Since finitely generated...
Non-amenable finitely presented torsion-by-cyclic groups