Separable subgroups have bounded packing
Abstract: In this paper, we prove that separable subgroups have bounded packing in ambient groups. The notion bounded packing was introduced by Hruska and Wise, and, in particular, our result confirms a conjecture of theirs which states that each subgroup of a virtually polycyclic group has the bounded packing property.
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- M. Hall, Coset representations in free groups. Trans. Amer. Math. Soc., 67 (1949), 421-432. MR 0032642 (11:322e)
- K. A. Hirsch, On infinite soluble groups. I. Proc. London Math. Soc., s2-44(1) (1938), 53-60.
- G. Hruska and D. Wise, Packing subgroups in relatively hyperbolic groups. Geom. Topol., 13(4) (2009), 1945-1988. MR 2497315 (2010c:20053)
- A. I. Mal'cev, On homomorphisms onto finite groups. American Mathematical Society Translations, Ser. 2, vol. 119, 1983, 67-79.
Affiliation: College of Mathematics and Econometrics, Hunan University, Changsha, Hunan 410082, People’s Republic of China
Address at time of publication: U.F.R. de Mathematiques, Universite de Lille 1, 59655 Villeneuve D’Ascq Cedex, France
Keywords: Bounded packing, separable, polycyclic group
Received by editor(s): August 24, 2010
Published electronically: March 2, 2011
Additional Notes: The author is supported by the China-funded Postgraduates Studying Abroad Program for Building Top University. This research was supported by the National Natural Science Foundation of China (No. 11081059).
Communicated by: Alexander N. Dranishnikov
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.