Undistorted solvable linear groups

Abels, Herbert; Alperin, Roger

doi:10.1090/S0002-9947-2011-05237-2

Undistorted solvable linear groups
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by Herbert Abels and Roger Alperin PDF

Trans. Amer. Math. Soc. 363 (2011), 3185-3210

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

H. Abels, Reductive groups as metric spaces, Groups: topological, combinatorial and arithmetic aspects, London Math. Soc. Lecture Note Ser., vol. 311, Cambridge Univ. Press, Cambridge, 2004, pp. 1–20. MR 2073343, DOI 10.1017/CBO9780511550706.002
Herbert Abels, Kompakt definierbare topologische Gruppen, Math. Ann. 197 (1972), 221–233 (German). MR 315039, DOI 10.1007/BF01428228
Armand Borel and Jacques Tits, Groupes réductifs, Inst. Hautes Études Sci. Publ. Math. 27 (1965), 55–150 (French). MR 207712, DOI 10.1007/BF02684375
N. Bourbaki, Éléments de mathématique. Topologie générale. Chapitres 1 à 4, Hermann, Paris, 1971. MR 0358652
Jean-Pierre Conze and Yves Guivarc’h, Remarques sur la distalité dans les espaces vectoriels, C. R. Acad. Sci. Paris Sér. A 278 (1974), 1083–1086 (French). MR 339108
M. Gromov, Asymptotic invariants of infinite groups, Geometric group theory, Vol. 2 (Sussex, 1991) London Math. Soc. Lecture Note Ser., vol. 182, Cambridge Univ. Press, Cambridge, 1993, pp. 1–295. MR 1253544
Yves Guivarc’h, Croissance polynomiale et périodes des fonctions harmoniques, Bull. Soc. Math. France 101 (1973), 333–379 (French). MR 369608, DOI 10.24033/bsmf.1764
Sami Mustapha, Distorsion des distances dans les groupes $p$-adiques, Bull. Sci. Math. 124 (2000), no. 3, 175–191 (French). MR 1753262, DOI 10.1016/S0007-4497(00)00129-9
D. V. Osin, Exponential radicals of solvable Lie groups, J. Algebra 248 (2002), no. 2, 790–805. MR 1882124, DOI 10.1006/jabr.2001.9036
L. S. Pontryagin, Topological groups, Gordon and Breach Science Publishers, Inc., New York-London-Paris, 1966. Translated from the second Russian edition by Arlen Brown. MR 0201557
M. S. Raghunathan, Discrete subgroups of Lie groups, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 68, Springer-Verlag, New York-Heidelberg, 1972. MR 0507234, DOI 10.1007/978-3-642-86426-1
Nicholas Th. Varopoulos, Distance distortion on Lie groups, Random walks and discrete potential theory (Cortona, 1997) Sympos. Math., XXXIX, Cambridge Univ. Press, Cambridge, 1999, pp. 320–357. MR 1802438
Nicholas Th. Varopoulos, 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 (French, with English and French summaries). MR 1396633