Hostname: page-component-cd9895bd7-gvvz8 Total loading time: 0 Render date: 2024-12-27T22:10:10.005Z Has data issue: false hasContentIssue false
  • English
  • Français

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 [email protected]@mcs.st-and.ac.uk
NIK RUšKUC
Affiliation:
Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, United [email protected]@mcs.st-and.ac.uk
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)