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Products of three idempotent transformations

Published online by Cambridge University Press:  17 April 2009

R. P. Sullivan  and
Rachel Thomas
R. P. Sullivan
Affiliation:
Department of Mathematics and Statistics, University of Western Australia, Nedlands WA 6009, Australia
Rachel Thomas
Affiliation:
Department of Mathematics and Statistics, University of Western Australia, Nedlands WA 6009, Australia
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Abstract

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In 1988 Howie, Robertson and Schein characterised the transformations of a finite set X that can be written as a product of two or of three idempotent transformations of X; and in 1989 Saito did the same for products of four idempotents. In 1998 Thomas extended the characterisation of two idempotents to arbitrary sets, and here we characterise products of three idempotents in general. We also define a notion of complexity for transformations of any set and use it to provide a different solution to the three-idempotent problem.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 68 , Issue 1 , August 2003 , pp. 57 - 71
Copyright
Copyright © Australian Mathematical Society 2003

References

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