J Austral Math Soc Ser A 56 pp212--231, 1994.

On Free Products of Completely Regular Semigroups

Peter R. Jones

(Received 26 July 1991)

Abstract

The free product *_CRS_i of an arbitrary family of disjoint simple semigroups {S_i}_{i Î I}, within the variety CR of completely regular semigroups, is described by means of a theorem generalizing that of Kadourek and Polak for free completely regular semigroups. A notable consequence of the description is that all maximal subgroups of *_CRS_i are free, except for those in the factors S_i themselves. The general theorem simplifies in the case of free CR-products of groups and, in particular, free idempotent-generated completely regular semigroups.

1991 AMS Subject Classification: primary 20M05; secondary 08A50

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Authors

Peter R. Jones: Department of Mathematics, Statistics and Computer Science, Marquette University, Milwaukee, WI 53233, USA.

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