On F-inverse covers of finite-above inverse monoids

N. Szakács, M.B. Szendrei

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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 partial order and the least group congruence of M. © 2015 Elsevier Inc.
Original languageEnglish
Pages (from-to)42-65
Number of pages24
JournalJournal of Algebra
Publication statusPublished - 2016

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