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Properties of the subsemigroups of the bicyclic monoid

L. Descalço, N. Ruškuc (2008)

Czechoslovak Mathematical Journal

In this paper we study some properties of the subsemigroups of the bicyclic monoid B, by using a recent description of its subsemigroups. We start by giving necessary and sufficient conditions for a subsemigroup to be finitely generated. Then we show that all finitely generated subsemigroups are automatic and finitely presented. Finally we prove that a subsemigroup of B is residually finite if and only if it does not contain a copy of B.

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