Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

Remote Access
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Automorphisms of the ordered multiplicative group of positive rational numbers

Authors: A. M. W. Glass and Paulo Ribenboim
Journal: Proc. Amer. Math. Soc. 122 (1994), 15-18
MSC: Primary 06F20; Secondary 11J81, 20F60
MathSciNet review: 1195720
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We prove

Theorem. The only automorphism of the ordered multiplicative group of positive rational numbers is the trivial automorphism.

We also give other examples of multiplicative groups of real positive algebraic numbers whose only order-preserving automorphisms are trivial.

References [Enhancements On Off] (What's this?)

  • [1] M. Giraudet (ed.), First meeting on ordered groups and infinite permutation groups, problem sessions & abstracts, CIRM Luminy, France, July 1990.
  • [2] Alan Baker, Transcendental number theory, Cambridge University Press, London-New York, 1975. MR 0422171 (54 #10163)
  • [3] L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford-London-New York-Paris; Addison-Wesley Publishing Co., Inc., Reading, Mass.-Palo Alto, Calif.-London, 1963. MR 0171864 (30 #2090)
  • [4] H. Halberstam, Transcendental numbers, Math. Gaz. 58 (1974), 276–284. MR 0466034 (57 #5917)
  • [5] Serge Lang, Algebraic values of meromorphic functions. II, Topology 5 (1966), 363–370. MR 0202670 (34 #2530)
  • [6] K. Ramachandra, Contributions to the theory of transcendental numbers. I, II, Acta Arith. 14 (1967/68), 65-72; ibid. 14 (1967/1968), 73–88. MR 0224566 (37 #165)
  • [7] P. Ribenboim, Théorie des valuations, Presses Univ. Montréal, Montréal, 1964.
  • [8] M. Waldschmidt, Linear independence of logarithms of algebraic numbers, Mathematical Notes, Matscience Institute, Madras.

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 06F20, 11J81, 20F60

Retrieve articles in all journals with MSC: 06F20, 11J81, 20F60

Additional Information

PII: S 0002-9939(1994)1195720-5
Article copyright: © Copyright 1994 American Mathematical Society

Comments: Email Webmaster

© Copyright , American Mathematical Society
Contact Us · Sitemap · Privacy Statement

Connect with us Facebook Twitter Google+ LinkedIn Instagram RSS feeds Blogs YouTube Podcasts Wikipedia