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Explicit free subgroups of $\operatorname {Aut}(\mathbf R,\le )$

Author: Curtis D. Bennett
Journal: Proc. Amer. Math. Soc. 125 (1997), 1305-1308
MSC (1991): Primary 06F15; Secondary 20E05
MathSciNet review: 1363412
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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 $\operatorname {Aut} (\mathbf Q,\le )$.

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Curtis D. Bennett
Affiliation: Department of Mathematics, Bowling Green State University, Bowling Green, Ohio 43403

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
Article copyright: © Copyright 1997 American Mathematical Society