Abstract
We consider the question of membership of A ∨ G, where A and G are the pseudovarieties of finite aperiodic semigroups, and finite groups, respectively. We find a straightforward criterion for a semigroup S lying in a class of finite semigroups that are weakly abundant, to be in A ∨ G. The class of weakly abundant semigroups contains the class of regular semigroups, but is much more extensive; we remark that any finite monoid with semilattice of idempotents is weakly abundant. To study such semigroups we develop a number of techniques that may be of interest in their own right.
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Communicated by Mária B. Szendrei
This work was funded by the London Mathematical Society, the British Council and Project POCTI/0143/2007 of CAUL financed by FCT and FEDER.
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Fountain, J., Gomes, G. & Gould, V. Membership of A ∨ G for classes of finite weakly abundant semigroups. Period Math Hung 59, 9–36 (2009). https://doi.org/10.1007/s10998-009-9009-1
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DOI: https://doi.org/10.1007/s10998-009-9009-1