Abstract
The concept of a ∗-variety of congruences is introduced and related to ∗-variety of languages and variety of monoids. A systematic construction of increasingly complex ∗-varieties of congruences is presented. This construction is powerful enough to generate all monoids containing solvable groups. Some hierarchies occurring through this process are shown to correspond to well-known hierarchies of monoids, thus indicating that our construction is natural from an algebraic point of view. Some problems that remain open are also discussed.
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