Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Available in electronic format
Available in print format 		Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(e) ISSN 0002-9939(p)

     

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

Author(s): Curtis D. Bennett
Journal: Proc. Amer. Math. Soc. 125 (1997), 1305-1308.
MSC (1991): Primary 06F15; Secondary 20E05
MathSciNet review: 1363412
Retrieve article in: PDF
This article is available free of charge

Abstract | References | Similar articles | Additional information

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:

[D]
J. D. Dixon, Most finitely generated permutation groups are free, Bull. London Math. Soc. 22, 222-226 (1990). MR 91c:20005

[GM]
A. M. W. Glass and S. H. McCleary, Highly transitive representations of free groups and free products, Bull. Australian Math. Soc. 43, 19-36 (1991). MR 91m:20009

[GMR]
A. M. W. Glass, S. H. McClearly, and M. Rubin, Automorphism groups of countable highly homogeneous partially ordered sets, Mathematische Zeitschrift 214, 55-66 (1993). MR 94i:20005

[K]
F. Klein, Neue Beiträge zur Riemannischen Funktionentheorie, Math. Ann. 21, 141-218 (1883).

[LS]
R. C. Lyndon and P. E. Schupp, Combinatorial Group Theory, Springer-Verlag, Berlin (1977). MR 58:28182

[M]
A. M. Macbeath, Packings, free products, and residually finite groups, Proc. Cambridge Phil. Soc. 59, 555-558 (1963). MR 26:6237

[N]
B. H. Neumann, On ordered groups, American Journal of Math. 71, 1-18 (1949). MR 10:428a

[W]
S. White, The group generated by $x\mapsto x+1$ and $x\mapsto x^p$ is free, Journal of Algebra 118, 408-422 (1988). MR 90a:12014

Similar Articles:

Retrieve articles in Proceedings of the American Mathematical Society with MSC (1991): 06F15, 20E05

Retrieve articles in all Journals with MSC (1991): 06F15, 20E05

Additional Information:

Curtis D. Bennett
Affiliation: Department of Mathematics, Bowling Green State University, Bowling Green, Ohio 43403
Email: cbennet@math.bgsu.edu

DOI: 10.1090/S0002-9939-97-03693-9
PII: S 0002-9939(97)03693-9
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 of article: Copyright 1997, American Mathematical Society




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia