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Formations of inverse semigroups

Gomes, Gracinda M. S.; Nobre, Isabel J.

Semigroup Forum , 105 (2022), 217–243

This article explores a generalisation of the theory of formations of groups. Taking formations of groups as the starting point, formations of inverse semigroups are defined, as well as the wider classes of i-formations (i standing for idempotent-separating) and some classes of the kind named f-formations (f standing for fundamental). The relation between the nature of a class of groups and that of certain classes of inverse semigroups with associated groups in the first is discussed. The product of formations is considered, and a product like the Gaschutz’s product known for groups is presented for f-formations.