Hostname: page-component-8448b6f56d-qsmjn Total loading time: 0 Render date: 2024-04-25T06:42:37.597Z Has data issue: false hasContentIssue false

EMBEDDING IN A FINITE 2-GENERATOR SEMIGROUP

Part of: Semigroups

Published online by Cambridge University Press:  10 June 2016

PETER M. HIGGINS*
Affiliation:
Department of Mathematical Sciences, University of Essex, Wivenhoe Park, Colchester, Essex CO4 3SQ, UK e-mail: peteh@essex.ac.uk
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We augment the body of existing results on embedding finite semigroups of a certain type into 2-generator finite semigroups of the same type. The approach adopted applies to finite semigroups the idempotents of which form a band and also to finite orthodox semigroups.

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2016 

References

REFERENCES

1. Benzaken, C. and Mayr, H. C., Noti on de demi-bande: Demi-bandes de type deux, (French) Semigroup Forum 10 (2) (1975), 115128.Google Scholar
2. Evans, T., Embedding theorems for multiplicative systems and projective geometries, Proc. American Math. Soc 3 (1952), 614620.CrossRefGoogle Scholar
3. Hall, T. E., Inverse and regular semigroups and amalgamation: a brief survey, in Proc. of the Symposium on regular semigroups, Northern Illinois University, (1979), 49–79.Google Scholar
4. Higgins, P. M., Techniques of semigroup theory (OUP, Oxford, 1992).Google Scholar
5. Howie, J. M., Fundamentals of semigroup theory (OUP, Oxford, 1995).Google Scholar
6. Hunter, R. P., On Certain Two Generator Monoids, Semigroup Forum, Vol. 47 (1993), 96100.Google Scholar
7. Margolis, S., Maximal pseudovarieties of finite monoids and semigroups Russian Mathematics (Izvestiya VUZ, Matematika), 1995, 39:1.Google Scholar
8. McAlister, D. B., Stephen, J. B. and Vernitski, A., Embedding In in a 2-generator inverse subsemigroup of I n+2 , Proceedings of the Edinburgh Mathematical Society (2002) 45, 14.Google Scholar
9. Mian, A. M. and Chowla, S. D., On the B 2-sequences of Sidon, Proc. Nat. Acad. Sci. India A14 (1944), 34.Google Scholar
10. Neumann, B. H., Embedding theorems for semigroups, J. London Math. Soc. 35 (1960), (184–192).Google Scholar
11. Sierpinski, W., Sur les suites infinies de fonctions dêfinies dans les ensembles quelconques, Fund. Math. 24 (1935), 209212.CrossRefGoogle Scholar