J. Aust. Math. Soc. 83 (2007), no. 3, pp. 357–367.

On finite generation and presentability of Schützenberger products

Peter Gallagher Nik Ruškuc
School of Mathematics and Statistics
University of St Andrews
St Andrews
Scotland, UK
School of Mathematics and Statistics
University of St Andrews
St Andrews
Scotland, UK
Received 25 July 2005; revised 5 May 2006
Communicated by D. Easdown


The finite generation and presentation of Schützenberger products of semigroups are investigated. A general necessary and sufficient condition is established for finite generation. The Schützenberger product of two groups is finitely presented as an inverse semigroup if and only if the groups are finitely presented, but is not finitely presented as a semigroup unless both groups are finite.

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2000 Mathematics Subject Classification: primary 20M05; secondary 20M18
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