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A coherence theorem on Schützenberger groups

Published online by Cambridge University Press:  09 April 2009

Pierre Antoine Grillet
Pierre Antoine Grillet
Affiliation:
TulaneUniversity New Orleans, Louisiana 70118, U.S.A.
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It is well-known that, in any semigroup S, all the left and right Schützenberger groups of the ℋ-class contained in a fixed D class D of S are isomorphic to one group. We prove a sharper result: that, up to actionpreserving isomorphisms, all these Schützenberger groups and their classical isomorphisms are but one group and its identity isomorphism; thus, one group is essentially sufficient to describe not only all the Schützenberger groups of ℋ-classes in D, but their action on these ℋ-classes and classical isomorphisms as well.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 21 , Issue 2 , March 1976 , pp. 129 - 143
Copyright
Copyright © Australian Mathematical Society 1976

References

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