Skip Navigation

Journal of the London Mathematical Society 2002 66(3):623-640; doi:10.1112/S0024610702003599
© 2002 by London Mathematical Society
This Article
Right arrow Full Text (PDF)
Right arrow Alert me when this article is cited
Right arrow Alert me if a correction is posted
Services
Right arrow Email this article to a friend
Right arrow Similar articles in this journal
Right arrow Alert me to new issues of the journal
Right arrow Add to My Personal Archive
Right arrow Download to citation manager
Right arrowRequest Permissions
Google Scholar
Right arrow Articles by Müller, T. W.
Right arrow Articles by Puchta, J.-C.
Right arrow Search for Related Content
Social Bookmarking
Add to CiteULike   Add to Connotea   Add to Del.icio.us  
What's this?

© The London Mathematical Society

Character Theory of Symmetric Groups and Subgroup Growth of Surface Groups

Thomas W. Müller and Jan-Christoph Puchta

School of Mathematical Sciences, Queen Mary, University of London Mile End Road, London E1 4NS, t.w.muller{at}qmul.ac.uk
Mathematical Institute, University of Oxford 24–29 St Giles’, Oxford OX1 3LB, puchta{at}maths.ox.ac.uk

Received 14 September 2001. Revision received 2 February 2002.

Results from the character theory of symmetric groups are used to obtain an asymptotic estimate for the subgroup growth of fundamental groups of closed 2-manifolds. The main result implies an affirmative answer, for the class of groups investigated, to a question of Lubotzky's concerning the relationship between the subgroup growth of a one-relator group and that of a free group of appropriately chosen rank. As byproducts, an interesting statistical property of commutators in symmetric groups and the fact that in a ‘large’ surface group almost all finite index subgroups are maximal are obtained, among other things. The approach requires an asymptotic estimate for the sum {Sigma}1/({chi}{lambda}(1))s taken over all partitions {lambda} of n with fixed s ≥ 1, which is also established.


Add to CiteULike CiteULike   Add to Connotea Connotea   Add to Del.icio.us Del.icio.us    What's this?




Disclaimer:
Please note that abstracts for content published before 1996 were created through digital scanning and may therefore not exactly replicate the text of the original print issues. All efforts have been made to ensure accuracy, but the Publisher will not be held responsible for any remaining inaccuracies. If you require any further clarification, please contact our Customer Services Department.