2 citations · 5 across the 5 of their papers we have counts for
3 papers · 2 filters
Simple groups with infinite verbal width and the same positive theory as free groups
Montserrat Casals-Ruiz, Albert Garreta, Ilya Kazachkov +1
In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abelian free group. In particular, these…
On the positive theory of groups acting on trees
Montserrat Casals-Ruiz, Albert Garreta, Javier de la Nuez González
We study the positive theory of groups acting on trees and show that under the presence of weak small cancellation elements, the positive theory of the group is trivial, i.e. coinc…
On equations and first-order theory of one-relator monoids
Albert Garreta, Robert D. Gray
We investigate systems of equations and the first-order theory of one-relator monoids. We describe a family of one-relator monoids of the form $\langle A\mid w=1\rang…