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Products of idempotents in finite full transformation semigroups

Published online by Cambridge University Press:  14 November 2011

J. M. Howie
J. M. Howie
Affiliation:
Mathematical Institute, University of St Andrews†
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Synopsis

If |X| = n and α is a singular mapping in J(X), define c(α) to be the number of cyclic orbits of α and f(α) to be the number of fixed points. Then α is expressible as a product of n + c(α)−f(α) idempotents of rank n − 1, and no smaller number of idempotents of rank n − 1 will suffice. The maximum possible value of n + c(α)–f(α) is [3/2(n − 1)], which is thus a best possible global lower bound for the number of idempotents required to generate a singular element of J(X).

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 86 , Issue 3-4 , 1980 , pp. 243 - 254
Copyright
Copyright © Royal Society of Edinburgh 1980

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References

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