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Soluble Semigroups

Published online by Cambridge University Press:  09 April 2009

Peter G. Trotter
Peter G. Trotter
Affiliation:
Mathematics Department University of Tasmania Hobart, Tasmania
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The cancellation law is a necessary condition for a semigroup to be embedded in a group. In general, this condition is not sufficient; necessary and sufficient conditions are rather complicated (see [1]). It is, therefore, of interest to find large classes of semigroups for which the cancellation law is sufficient to ensure embeddability in a group.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 13 , Issue 1 , February 1972 , pp. 114 - 118
Copyright
Copyright © Australian Mathematical Society 1972

References

[1]Clifford, A. H. and Preston, G. B., The algebraic theory of semigroups, vols. 1 and 2, (Amer. Math. Soc. Mathematical Surveys 7, Providence, 1961 and 1967).Google Scholar
[2]Mal'cev, A. I., ‘Nilpotent semigroups’, Ivanov. Gos. Ped. Inst. Uč. Zap. Fiz.-Mat. Nauki, 4 (1953), 107–111.Google Scholar