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Embeddings into finite idempotent-generated semigroups: some arithmetical results

Published online by Cambridge University Press:  20 January 2009

Emilia Giraldes  and
John M. Howie
Emilia Giraldes
Affiliation:
Universidade Nova de Lisboa
John M. Howie
Affiliation:
University of St Andrews
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A semiband is defined as a semigroup generated by idempotents. It is known that every finite semigroup is embeddable in a finite semiband. For a class C of semigroups and an integer n≧2, the number σC (n) is defined as the smallest k with the property that every semigroup of order n in the class C is embeddable in a semiband of order not exceeding k. It is shown that for the class Gp of groups σGp(n) = nq(ρGp(n)), where

and

Estimates are known (and are quoted) for the function q. Estimates are considered for the function pC for various C

It is shown also that if C0S, CS denote respectively the classes of completely 0-simple and completely simple semigroups, then

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 34 , Issue 2 , June 1991 , pp. 259 - 269
Copyright
Copyright © Edinburgh Mathematical Society 1991

References

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