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Nilpotents in semigroups of partial transformations

Published online by Cambridge University Press:  17 April 2009

R. P. Sullivan
R. P. Sullivan
Affiliation:
Department of Mathematics, University of Western Australia, Nedlands 4009Australia
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In 1987, Sullivan determined when a partial transformation α of an infinite set X can be written as a product of nilpotent transformations of the same set: he showed that when this is possible and the cardinal of X is regular then α is a product of 3 or fewer nilpotents with index at most 3. Here, we show that 3 is best possible on both counts, consider the corresponding question when the cardinal of X is singular, and investigate the role of nilpotents with index 2. We also prove that the nilpotent-generated semigroup is idempotent-generated but not conversely.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 55 , Issue 3 , June 1997 , pp. 453 - 467
Copyright
Copyright © Australian Mathematical Society 1997

References

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