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, Volume 18, Issue 1, pp 1–13 | Cite as

One parameter subgroups and nonstandard analysis

  • Michael Singer


We present here a discussion from a nonstandard viewpoint of some aspects of the theory of locally compact groups without small subgroups, as relevant to the solution of Hilbert's fifth problem. For background on nonstandard analysis we refer to Robinson [4].


Number Theory Algebraic Geometry Topological Group Compact Group Small Subgroup 
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  1. [1]
    HALL, P. Some sufficient conditions for a group to be nilpotent. Illinois J. Math. (2) 1958, 787–801.Google Scholar
  2. [2]
    KAPLANSKY, I. Lie algebras and locally compact groups. Chicago Lectures in Mathematics, 1971.Google Scholar
  3. [3]
    MONTGOMERY, D. and ZIPPIN, L. Topological Transformation Groups. Interscience Tracts in Pure and Applied Mathematics, 1955.Google Scholar
  4. [4]
    ROBINSON, A. Nonstandard analysis. North-Holland, 1966.Google Scholar

Copyright information

© Springer-Verlag 1976

Authors and Affiliations

  • Michael Singer
    • 1
  1. 1.Department of MathematicsThe Ohio State UniversityColumbusUSA

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