Explicit free subgroups of $\operatorname {Aut}(\mathbf {R},\le )$
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- by Curtis D. Bennett PDF
- Proc. Amer. Math. Soc. 125 (1997), 1305-1308 Request permission
Abstract:
In this note for any finite $n>1$, we give an explicit free subgroup of rank $n$ of the groups of ordered permutations of the reals $(\operatorname {Aut}(\mathbf R,\le ))$ for which the proof that the subgroup is free is elementary. Moreover, this example naturally generalizes to the group $\operatorname {Aut}(\mathbf Q,\le )$.References
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Additional Information
- Curtis D. Bennett
- Affiliation: Department of Mathematics, Bowling Green State University, Bowling Green, Ohio 43403
- Email: cbennet@math.bgsu.edu
- Received by editor(s): July 27, 1994
- Received by editor(s) in revised form: November 17, 1995
- Additional Notes: The author gratefully acknowledges the support of an NSF postdoctoral fellowship.
- Communicated by: Andreas R. Blass
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 1305-1308
- MSC (1991): Primary 06F15; Secondary 20E05
- DOI: https://doi.org/10.1090/S0002-9939-97-03693-9
- MathSciNet review: 1363412