Abstract
The finitary power semigroup of a semigroup S, denoted Pf(S), is the set of finite subsets of S with respect to the usual set multiplication. Semigroups with finitely generated finitary power semigroups are characterised in terms of three other properties. From this statement there are drawn several corollaries. It follows that Pf(S) is not finitely generated if S is infinite and in any of the following classes: commutative; Bruck-Reilly extensions; inverse semigroups that contain an infinite group; completely zero-simple; completely regular.
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