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On free products of completely regular semigroups

Part of: Semigroups Algebraic structures

Published online by Cambridge University Press:  09 April 2009

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

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

MSC classification

Secondary: 20M05: Free semigroups, generators and relations, word problems 08A50: Word problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 56 , Issue 2 , April 1994 , pp. 212 - 231
Copyright
Copyright © Australian Mathematical Society 1994

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