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FINITARY POWER SEMIGROUPS OF INFINITE GROUPS ARE NOT FINITELY GENERATED

Published online by Cambridge University Press:  01 June 2005

PETER GALLAGHER  and
NIK RUšKUC
PETER GALLAGHER
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, United Kingdompeterg@mcs.st-and.ac.uknik@mcs.st-and.ac.uk
NIK RUšKUC
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, United Kingdompeterg@mcs.st-and.ac.uknik@mcs.st-and.ac.uk
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Abstract

For a semigroup $S$, the finitary power semigroup of $S$, denoted $P_f(S)$, consists of all finite subsets of $S$ under the usual multiplication. The main result of this paper asserts that $P_f(G)$ is not finitely generated for any infinite group $G$.

Keywords

20M05 (primary)20M3020F99 (secondary)
Type
Papers
Information
Bulletin of the London Mathematical Society , Volume 37 , Issue 3 , June 2005 , pp. 386 - 390
Copyright
© The London Mathematical Society 2005

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