Formations of orthodox semigroups
Gomes, Gracinda M. S.; Ana-Catarina C. Monteiro
Semigroup Forum, 107 (2023), 651–679
Taking formations of groups and of inverse semigroups as the starting point, formations of orthodox semigroups are defined, as well as the wider class of i-formations (i standing for idempotent-separating).
The relation between the nature of a class of inverse semigroups $\mathcal{F}$ [of groups $\mathcal{G}$] and that of certain classes of orthodox semigroups with associated inverse semigroups in $\mathcal{F}$ [groups in $\mathcal{G}$] is discussed.
The product of formations of orthodox semigroups, in particular of $R$-unipotent semigroups, is considered, and a product like the Gasch{\"u}tz´s product known for groups is presented for i-formations.
The paper concludes with a list of questions.
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