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Finite zero-simple semigroups over an elementary abelian group

Published online by Cambridge University Press:  17 April 2009

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

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Finite O-simple semigroups with a Rees representation over an elementary abelian group are considered. The isomorphism classes of such semigroups with class graph γ and coefficient group of order pd are shown to correspond to the orbits under the automorphism group of γ of those subspaces of the circuit space of γ over Zp which have codimension at most d. A semigroup interpretation of the inclusion relation between subspaces is given and results are obtained on the structure of the automorphism group and the enumeration of the semigroups under consideration.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 18 , Issue 2 , April 1978 , pp. 211 - 220
Copyright
Copyright © Australian Mathematical Society 1978

References

[1]Biggs, Norman, Algebraic graph theory (Cambridge Tracts in Mathematics, 67. Cambridge University Press, Cambridge, 1974).Google Scholar
[2]Houghton, C.H., “Completely 0-simple semigroups and their associated graphs and groups”, Semigroup Forum 14 (1977), 41–67.CrossRefGoogle Scholar
[3]Houghton, C.H., “Counting completely O-simple and completely simple semigroups”, Proc. Roy. Soc. Edinburgh Ser. A (to appear).Google Scholar
[4]Howie, J.M., Introduction to semigroup theory (Academic Press [Harcout Brace Jovanovich], London, New York, San Francisco, 1976).Google Scholar
[5]Maunder, C.R.F., Algebraic topology (Van Nostrand, London, New York, Cincinnati, Toronto, Melbourne, 1970).Google Scholar
[6]Rees, D., “On semi-groups”, Proc. Cambridge Philos. Soc. 36 (1940), 387–400.Google Scholar