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Free generators in free inverse semigroups

Published online by Cambridge University Press:  17 April 2009

N.R. Reilly
N.R. Reilly
Affiliation:
Department of Mathematics, Simon Fraser University, Burnaby, British Columbia, Canada.
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Abstract

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Using the characterization of the free inverse semigroup F on a set X, given by Scheiblich, a necessary and sufficient condition is found for a subset K of an inverse semigroup S to be a set of free generators for the inverse sub semigroup of S generated by K. It is then shown that any non-idempotent element of F generates the free inverse semigroup on one generator and that if |X| > 2 then F contains the free inverse semigroup on a countable number of generators. In addition, it is shown that if |X| = 1 then F does not contain the free inverse semigroup on two generators.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 7 , Issue 3 , December 1972 , pp. 407 - 424
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Clifford, A.H. and Preston, G.B., The algebraic theory of semigroups (Math. Surveys 7 (I). Amer. Math. Soc., Providence, Rhode Island, 1961).Google Scholar
[2]Eberhart, Carl and Selden, John, “One parameter inverse semigroups”, Trans. Amer. Math. Soc. (to appear).Google Scholar
[3]McAlister, D.B., “A homomorphism theorem for semigroups”, J. London Math. Soc. 43 (1968), 355–366.CrossRefGoogle Scholar
[4]Munn, W.D., “A certain sublattice of the lattice of congruences on a regular semigroup”, Proc. Cambridge Philos. Soc. 60 (1964), 385–391.CrossRefGoogle Scholar
[5]Шайн, Б.М. [S˘aĭn, B.M.], “К теории обобщенных групп” [On the theory of generalized groups], Dokl. Akad. Nauk SSSR 153 (1963), 296–299.Google ScholarPubMed
[6]Scheiblich, H.E., “Free inverse semigroups”, (to appear).Google Scholar
[7]Schenkman, Eugene, Group theory (Van Nostrand, Princeton, New Jersey; Toronto; New York; London; 1965).Google Scholar