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Let Ω Ω be the semigroup of all mappings of a countably infinite set Ω. If U and V are subsemigroups of Ω Ω , then we write U ≈ V if there exists a finite subset F of Ω Ω such that the subgroup generated by U and F equals that generated by V and F. The relative rank of U in Ω Ω is the least cardinality of a subset A of Ω Ω such that the union of U and A… (More)

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