4 papers
Shirshov's amalgamated free product and generic nilpotent groups
Christian d'Elbée, Isabel Müller, Nicholas Ramsey +1
In earlier work, the authors gave a construction and description of an amalgamated free product of filtered Lie algebras within a fixed nilpotency class, based on an intricate indu…
Cofinality of Regular Tournaments
Omar Hatem, Sara Mohamed, Isabel Müller +1
We show that the class of all finite regular tournaments is cofinal in the class of finite tournaments. In addition, we establish cofinality results for certain special subclasses…
A Group with Exactly One Noncommutator
Omar Hatem, Daoud Siniora
The question of whether there exists a finite group of order at least three in which every element except one is a commutator has remained unresolved in group theory. In this artic…
A two-sorted theory of nilpotent Lie algebras
Christian d'Elbée, Isabel Müller, Nicholas Ramsey +1
We prove the existence of a model companion of the two-sorted theory of -nilpotent Lie algebras over a field satisfying a given theory of fields. We describe a language in which…