Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

   
 
 

 

Undistorted solvable linear groups


Authors: Herbert Abels and Roger Alperin
Journal: Trans. Amer. Math. Soc. 363 (2011), 3185-3210
MSC (2000): Primary 20G99, 20G25, 22E99, 22E25
DOI: https://doi.org/10.1090/S0002-9947-2011-05237-2
Published electronically: January 3, 2011
MathSciNet review: 2775803
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We discuss distortion of solvable linear groups over a locally compact field and provide necessary and sufficient conditions for a subgroup to be undistorted when the field is of characteristic zero.


References [Enhancements On Off] (What's this?)

  • 1. Abels, H., Reductive groups as metric spaces. London Math. Soc. Lecture Note Ser., 311 (2004), 1-20. MR 2073343 (2005i:20073)
  • 2. Abels, H. Kompakt definierbare topologische Gruppen Math. Ann. 197 (1972), 221-233. MR 0315039 (47:3588)
  • 3. Borel, A. and Tits, J., Groupes réductifs, Inst. Hautes Études Sci. Publ. Math., 27 (1965), 55-150. MR 0207712 (34:7527)
  • 4. Bourbaki N., Éléments de mathématique. Topologie générale. Chapitres 1 à 4, Hermann, Paris, (1971), xv+357 pp. MR 0358652 (50:11111)
  • 5. Conze, J.-P. and Guivarc'h, Y., Remarques sur la distalité dans les espaces vectoriels, C.R. Acad. Sci. Paris Sér. A, 278 (1974), 1083-1086. MR 0339108 (49:3871)
  • 6. Gromov, M., Asymptotic invariants of infinite groups. Geometric group theory, Vol. 2 (Sussex, 1991), 1-295, London Math. Soc. Lecture Note Ser., 182, Cambridge Univ. Press, Cambridge, 1993. MR 1253544 (95m:20041)
  • 7. Guivarc'h, Y., Croissance polynomiale et périodes des fonctions harmoniques, Bull. Soc. Math. France, 101 (1973), 333-379. MR 0369608 (51:5841)
  • 8. Mustapha, Sami, Distorsion des distances dans les groupes $ p$-adiques, Bull. Sci. Math., 124 (2000), no. 3, 175-191. MR 1753262 (2001f:22028)
  • 9. Osin, D.V., Exponential radicals of solvable Lie groups, J. Algebra, 248 (2002), 790-805. MR 1882124 (2002m:22008)
  • 10. Pontryagin, L., Topological groups, Translated from the second Russian edition by Arlen Brown, Gordon and Breach Science Publishers, New York (1966), xv+543. MR 0201557 (34:1439)
  • 11. Raghunathan, M.S., Discrete subgroups of Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, 68, Springer-Verlag, New York (1972), ix+227. MR 0507234 (58:22394a)
  • 12. Varopoulos, Nicholas Th., Distance distortion on Lie groups. Random walks and discrete potential theory (Cortona, 1997), 320-357, Sympos. Math., XXXIX, Cambridge Univ. Press, Cambridge, 1999. MR 1802438 (2002g:22022)
  • 13. Varopoulos, Nicholas Th., Sur la distorsion de distances des sous-groupes des groupes de Lie, C.R. Acad. Sci. Paris Sér. I Math., 322 (1996), no. 11, 1025-1026. MR 1396633 (97d:22010)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2000): 20G99, 20G25, 22E99, 22E25

Retrieve articles in all journals with MSC (2000): 20G99, 20G25, 22E99, 22E25


Additional Information

Herbert Abels
Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
Email: abels@math.uni-bielefeld.de

Roger Alperin
Affiliation: Department of Mathematics, San Jose State University, San Jose, California 95192
Email: alperin@math.sjsu.edu

DOI: https://doi.org/10.1090/S0002-9947-2011-05237-2
Received by editor(s): July 29, 2009
Published electronically: January 3, 2011
Additional Notes: The authors thank the SFB701 at Bielefeld and also MSRI for partial support during the period of research and preparation of this paper.
Article copyright: © Copyright 2011 by the authors

American Mathematical Society