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Idempotent generators 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

It was proved by Howie in 1966 that , the semigroup of all singular mappings of a finite set X into itself, is generated by its idempotents. Implicit in the method of proof, though not formally stated, is the result that if |X| = n then the n(n – 1) idempotents whose range has cardinal n – 1 form a generating set for. Here it is shown that if n ≧ 3 then a minimal set M of idempotent generators for contains ½n(n–1) members. A formula is given for the number of distinct sets M.

Information

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 81 , Issue 3-4 , 1978 , pp. 317 - 323
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Harary, F.Graph theory. (Reading, Mass.: Addison-Wesley, 1969).CrossRefGoogle Scholar
2Harary, F. and Palmer, E. M.Graphical enumeration. (New York: Academic Press, 1973).Google Scholar
3Howie, J. M.An introduction to semigroup theory. (London: Academic Press, 1976).Google Scholar
4Howie, J. M.The subsemigroup generated by the idempotents of a full transformation semigroup. J. London Math. Soc. 41 (1966), 707–716.CrossRefGoogle Scholar
5Moon, John W.Topics on tournaments. (New York: Holt, Rinehart and Winston, 1968).Google Scholar