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Semigroups of high rank

Published online by Cambridge University Press:  20 January 2009

Emilia Giraldes  and
John M. Howie
Emilia Giraldes
Affiliation:
Departamento de Matemática Faculdade de CiênciasUniversidade de Lisboa1700 Lisboa, Portugal
John M. Howie
Affiliation:
Mathematical Institute University of St AndrewsNorth HaughSt Andrews, Scotland
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By the rank r(S) of a finite semigroup S we shall mean the minimum cardinality of a set of generators ofS. For a group G, as remarked in [3], one has r(G)≦log2|G|, the bound being attained when G is an elementary abelian 2-group. By contrast, we shall see that there exist finite semigroups S for which r(S)≧|S| – 1. In the hope that it will not be considered too whimsical, we shall refer to a finite semigroup S of maximal rank (i.e. for which r(S) = |S|) as royal; a semigroup of next-to-maximal rank (i.e. for which r(S) = |S|–1) will be called noble.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 28 , Issue 1 , February 1985 , pp. 13 - 34
Copyright
Copyright © Edinburgh Mathematical Society 1985

References

REFERENCES

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