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Counting completely 0-simple and completely simple semigroups

Published online by Cambridge University Press:  14 November 2011

C. H. Houghton
Affiliation:
Department of Pure Mathematics, University College, Cardiff

Synopsis

Formulae are derived for the numbers of completely 0-simple and completely simple semigroups with m ℒ-classes, n ℜ-classes and underlying finite group G.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 1978

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References

1Burnside, W.Theory of groups of finite order, 2nd edn. (Cambridge: Univ. Press, 1911).Google Scholar
2Harary, F.On the number of bi-colored graphs. Pacific J. Math. 8 (1958), 743755.CrossRefGoogle Scholar
3Harary, F. and Palmer, E. M.Graphical enumeration (New York: Academic Press, 1973).Google Scholar
4Howie, J. M.An introduction to semigroup theory (London: Academic Press, 1976).Google Scholar
5Houghton, C. H.Completely 0-simple semigroups and their associated graphs and groups. Semigroup Forum 14 (1977), 4167.CrossRefGoogle Scholar
6Rees, D.On semi-groups. Proc. Cambridge Philos. Soc. 36 (1940), 387400.CrossRefGoogle Scholar