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Automorphisms of normal partial transformation semigroups

Published online by Cambridge University Press:  18 May 2009

Inessa Levi
Inessa Levi*
Affiliation:
Department of Mathematics, University of Louisville, Louisville, Kentucky 40292, U.S.A.
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We let X be an arbitrary infinite set. A semigroup S of total or partial transformations of X is called -normal if hSh-1 = S, for all h in , the symmetric group on X. For example, the full transformation semigroup , the semigroup of all partial transformations , the semigroup of all 1–1 partial transformations and all ideals of and are -normal.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 29 , Issue 2 , July 1987 , pp. 149 - 157
Copyright
Copyright © Glasgow Mathematical Journal Trust 1987

References

1. Gluskin, L. M., Ideals of semigroups of transformations, Mat. Sb. (N.S.) 47 (89) (1959), 111–130.Google Scholar
2. Levi, I., Schein, B. M., Sullivan, R. P. and Wood, G. R., Automorphisms of Baer-Levi semigroups, J. London Math. Soc. (2) 28 (1983), 492–495.CrossRefGoogle Scholar
3. Levi, I., Automorphisms of normal transformation semigroups, Proc. Edinburgh Math. Soc., to appear.Google Scholar
4. Liber, A. E., On symmetric generalized groups, Mat. Sb. (N.S.) 33 (75) (1953), 531–544.Google Scholar
5. Mal'cev, A. I., Symmetric groupoids, Mat. Sb. (N.S.) 31 (73) (1952), 136–151, translated in Amer. Math. Soc. Transl. 113 (1979), 235–250.Google Scholar
6. Schein, B. M., Symmetric semigroups of one-to-one transformations, Second all-union symposium on the theory of semigroups, Summaries of Talks (Sverdlovsk, 1979), 99.Google Scholar
7. Schein, B. M., Symmetric semigroups of transformations, Abstracts Amer. Math. Soc. 5 (1980), 476.Google Scholar
8. Shutov, E. G., On semigroups of almost identical mappings, Dokl. Akad. Nauk SSSR 134 (1960), 292–295.Google Scholar
9. Shutov, E. G., Homomorphisms of the semigroup of all partial transformations, Izv. Vysš. Učebn. Zaved. Matematika, 1961, no. 3 (22), 177–184.Google Scholar
10. Schreier, J., Uber Abbildungen einer abstrakten Menge auf ihre Teilmengen, Fund. Math. 28 (1937), 261–264.CrossRefGoogle Scholar
11. Sullivan, R. P., Automorphisms of transformation semigroups, J. Austral. Math. Soc. Ser. A. 20 (1975), 77–84.CrossRefGoogle Scholar