Abstract
We characterise (residually-finite) groups which possess less than n subgroups of index n for almost all n ∈ ℕ.
Similar content being viewed by others
References
Klaas, G., Leedham-Green, C.R., Plesken, W.: Linear pro-p-groups of finite width. Lecture Notes in Mathematics 1674, Springer Verlag, Berlin-Heidelberg, 1997
Klopsch, B.: Zeta functions related to the pro-p group SL11(Δ p ). Math. Proc. Camb. Phil. Soc. 135, 45–57 (2003)
Klopsch, B.: Pro-p groups with linear subgroup growth. Math. Z. 245, 335–370 (2003)
Klopsch, B.: On the Lie theory of p-adic analytic groups. Math. Z. 249, 713–730 (2005)
Leedham-Green, C.R., McKay, S.: The Structure of Groups of Prime Power Order. London Mathematical Society Monographs, New Series, Vol. 27, Oxford Science Publications, 2002
Lubotzky, A., Segal, D.: Subgroup Growth. Progress in Mathematics, Vol. 212, Birkhäuser, Basel, 2003
Prasad, G., Raghunathan, M.S.: Topological central extensions of SL1(D). Invent. Math. 92, 645–689 (1988)
Riehm, C.: The norm 1 group of p-adic division algebra. Am. J. Math. 92, 499–523 (1970)
Robinson, D.: A course in the theory of groups. Graduate Texts in Mathematics, Vol. 80, Springer, New York, 1982
Shalev, A.: Groups whose subgroup growth is less than linear. Int. J. Algebra Comput. 7, 77–91 (1997)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Klopsch, B. Groups with less than n subgroups of index n. Math. Ann. 333, 67–85 (2005). https://doi.org/10.1007/s00208-005-0665-z
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00208-005-0665-z