Transactions of the American Mathematical Society

Author(s): E. F. Robertson; N. Ruskuc; J. Wiegold
Journal: Trans. Amer. Math. Soc. 350 (1998), 2665-2685.
MSC (1991): Primary 20M05
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Abstract: The purpose of this paper is to give necessary and sufficient conditions for the direct product of two semigroups to be finitely generated, and also for the direct product to be finitely presented. As a consequence we construct a semigroup $S$

of order 11 such that $S\times T$ is finitely generated but not finitely presented for every finitely generated infinite semigroup $T$

. By way of contrast we show that, if $S$

and

belong to a wide class of semigroups, then $S\times T$ is finitely presented if and only if both $S$

and

are finitely presented, exactly as in the case of groups and monoids.

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E. F. Robertson
Affiliation: Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland
Email: efr@st-and.ac.uk

N. Ruskuc
Affiliation: Mathematical Institute, University of St Andrews, St Andrews KY16 9SS, Scotland
Email: nr1@st-and.ac.uk

J. Wiegold
Affiliation: School of Mathematics, University of Wales, College of Cardiff, Senghenydd Road, Cardiff, CF2 4AG, Wales
Email: SMAJW@cardiff.ac.uk

DOI: 10.1090/S0002-9947-98-02074-1
PII: S 0002-9947(98)02074-1
Received by editor(s): September 24, 1996
Copyright of article: Copyright 1998, American Mathematical Society

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