Finitary Power Semigroups of Infinite Groups are not Finitely Generated |
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| Authors: | Gallagher Peter; Ruskuc Nik |
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| Institution: | Mathematical Institute, University of St Andrews St Andrews KY16 9SS, United Kingdom; peterg{at}mcs.st-and.ac.uk, nik{at}mcs.st-and.ac.uk |
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| Abstract: | For a semigroup S, the finitary power semigroup of S, denotedPf(S), consists of all finite subsets of S under the usual multiplication.The main result of this paper asserts that Pf(G) is not finitelygenerated for any infinite group G. 2000 Mathematics SubjectClassification 20M05 (primary), 20M30, 20F99 (secondary). |
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