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The Hope property and free products of semigroups

Part of: Semigroups

Published online by Cambridge University Press:  09 April 2009

P. R. Jones
P. R. Jones
Affiliation:
Mathematics DepartmentUniversity of Western Australia Nedlands, Western AustraliaAustralia6009
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Abstract

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The free product of two Hopfian groups (in the category of groups) need not be Hopfian. We prove, by elementary methods, that the free product of two simple Hopfian inverse semigroups is Hopfian. In particular the free product of any two Hopfian groups, in the category of inverse semigroups, is again Hopfian. In fact the same is true in the category of all semigroups.

MSC classification

Secondary: 20M05: Free semigroups, generators and relations, word problems
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 27 , Issue 3 , May 1979 , pp. 358 - 364
Copyright
Copyright © Australian Mathematical Society 1979

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