Explicit free subgroups of 𝐴𝑢𝑡(𝐑,≤)

Bennett, Curtis

doi:10.1090/S0002-9939-97-03693-9

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

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