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Normal growth of large groups

Authors:	Email author" target="_blank">T W?Müller Email author Email author" target="_blank">J-C?Schlage-Puchta Email author

Institution:	(1) School of Mathematical Sciences, Queen Mary, University of London, Mile End Road, E1 4NS London, United Kingdom;(2) Mathematisches Institut, Albert-Ludwigs-Universität, Eckerstr. 1, 79104 Freiburg, Germany

Abstract:	For a finitely generated group $\Gamma$, denote by $s_{n}^{\triangleleft}(\Gamma)$ the number of normal subgroups of index n. A. Lubotzky proved that for the free group F_r of rank r, $s_{n}^{\triangleleft}(F_r)$ is of type n^logn. We show that the same is true for a much larger class of groups. On the other hand we show that for almost all n, the inequality $s_{n}^{\triangleleft}(\Gamma)$ < $n^{r-1+\varepsilon}$ holds true for every r-generated group $\Gamma$.Received: 30 October 2002

Keywords:	20E07 11N64
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