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On when a topologically simple semigroup is simple

Published online by Cambridge University Press:  09 April 2009

Kermit Sigmon
Affiliation:
Department of Mathematics University of Florida Gainesville, Florida 32611
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Abstract

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The compact semigroups in which each topologically simple subsemigroup is simple are characterized as those in which no subgroup sontains an element of infinite order. It is also shown that a locally compact toplogically simple subsemigroup of a compact semigroup must be simple. The note closes with an open problem.

Subject classification (Amer. Math. Soc. (MOS) 1970): primary 22 A 15; secondary 20 M 10.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1978

References

Chow, H. L. (1975), “In a compact semigroup, are topologically simple subsemigroups also simple?Amer. Math. Monthly 82, 155156.CrossRefGoogle Scholar
Clark, W. E., Mukherjea, A. and Tserpes, N. A. (1975), “Is topologically simple simple? Semigroup Forum 11, 9093.Google Scholar
Hofmann, K. H. and Mostert, P. S. (1966), Elements of Compact Semigroups (Charles E. Merrill Books, Columbus, Ohio).Google Scholar
Miranda, A. B. Paalman-de (1970), Topological semigroups, 2nd ed. (Mathematisch Centrum Amsterdam).Google Scholar