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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)

In this paper, we consider the group Aut(Q, ≤) of order-automorphisms of the rational numbers, proving a result analogous to a theorem of Galvin's for the symmetric group. In an announcement, Khélif states that every countable subset of Aut(Q, ≤) is contained in an N-generated subgroup of Aut(Q, ≤) for some fixed N ∈ N. We show that the least such N is 2.… (More)

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