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On a family of simple ordered groups

Published online by Cambridge University Press:  09 April 2009

Vlastimil Dlab
Vlastimil Dlab
Affiliation:
Department of MathematicsInstitute of Advanced Studies Australian National University Canberra, A.C.T.
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In the present paper we shall consider some subgroups of (increasing) autohomeomorphisms of the closed real interval <0, 1>; mainly because of brevity, we shall defer discussing possible generalizations of our results to more general ordered fields.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 3 , August 1968 , pp. 591 - 608
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Chehata, C. G., ‘An algebraically simple ordered group’, Proc. London Math. Soc. 2 (1952), 183–197.CrossRefGoogle Scholar
[2]Everett, C. J. and Ulam, S., ‘On ordered groups’, Trans. Amer. Math. Soc. 57 (1945), 208–216.CrossRefGoogle Scholar
[3]Fuchs, L., Partially ordered algebraic systems (Pergamon Press, Oxford-London-New York-Paris, 1963).Google Scholar
[4]Higman, G., ‘On infinite simple permutation groups’, Publ. Math. Debrecen 3 (1954), 221–226.CrossRefGoogle Scholar
[5]Holland, Ch., ‘The lattice-ordered group of automorphisms of an ordered set’, Michigan Math. J. 10 (1963), 399–408.CrossRefGoogle Scholar
[6]Matsushita, S., ‘Sur la puissance des ordres dans un groupe libre’, Proc. Koninkl. Nederl. Akad. Wet. A, 56 (1953), 15–16.Google Scholar
[7]Schreier, J. and Ulam, S., ‘Eine Bemerkung über die Gruppe der topologischen Abbildungen der Kreislinie auf sich selbst’, Studia Math. 5 (1935), 155–159.CrossRefGoogle Scholar
[8]Teh, H. H., ‘Construction of orders in abelian groups’, Proc. Cambridge Philos. Soc. 57 (1961), 476–482.CrossRefGoogle Scholar