On F-inverse covers of finite-above inverse monoids

Abstract

Finite-above inverse monoids are a common generalization of finite inverse monoids and Margolis--Meakin expansions of groups. Given a finite-above $E$-unitary inverse monoid $M$ and a group variety $U$, we find a condition for $M$ and $U$, involving a construction of descending chains of graphs, which is equivalent to $M$ having an $F$-inverse cover via $U$. In the special case where $U=Ab$, the variety of Abelian groups, we apply this condition to get a simple sufficient condition for $M$ to have no $F$-inverse cover via $Ab$, formulated by means of the natural parial order and the least group congruence of $M$.

References in corpus (1)

• On the graph condition regarding the $F$-inverse cover problem

Cited by in corpus (2)

• Finite F-inveres covers do exist
• Finite approximation of free groups I: the $F$-inverse cover problem