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Real order-automorphism groups

Part of: Ordered sets

Published online by Cambridge University Press:  09 April 2009

E. C. Weinberg
E. C. Weinberg
Affiliation:
Department of Mathematics, University of Illinois, Urbana, Illinois 61801, U.S.A.
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Abstract

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By using the concept of tame embeddings of chains, a characterization is given of the subobjects of the lattice-ordered groups of order-automorphisms of the chains of rational and real numbers.

MSC classification

Secondary: 06A05: Total order
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 31 , Issue 3 , October 1981 , pp. 257 - 261
Copyright
Copyright © Australian Mathematical Society 1981

References

Arens, Richard (1951), ‘Ordered sequence spaces’, Portugal. Math. 10, 25–28.Google Scholar
Glass, A. M. W. (1976), Ordered permutation groups (Bowling Green State University).Google Scholar
Gurevich, Y. and Holland, W. C. (1981), ‘Recognizing the real line’, Trans. Amer. Math. Soc. 265, 527–534.Google Scholar
Holland, W. C. (1963), ‘The lattice-ordered group of automorphisms of an ordered set’, Michigan Math. J. 10, 399–408.Google Scholar
Sierpinski, W. (1958), Cardinal and ordinal numbers (Warsaw).Google Scholar
Weinberg, E. C. (1978), ‘Automorphism groups of minimal ηα-sets’, Boise conference on ordered algebraic structures, to appear.Google Scholar
Weinberg, E. C. (1967), ‘Embedding in a divisible lattice-ordered group’, J. London Math. Soc. 42, 504–506.Google Scholar