Abstract
We show that the semigroups Sk,ℓhaving semigroup presentations <a, b:abk= bℓa> are residually finite and finitely separable. Generally, these semigroups have finite separating images which are finite groups and other finite separating images which are semigroups of order-increasing transformations on a finite partially ordered set. These semigroups thus have vastly different residual and separability properties than the Baumslag–Solitar groups which contain them.
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