Normal Subgroup Growth of Linear Groups: the (G2; F4;E8)-Theorem
Group Theory
2011-08-05 v1
Abstract
Let G be a finitely generated group and M_n(G) the number of its normal subgroup subgroups of index at most n. For linear groups G we show that M_n(G) can grow polynomially in n only if the semisimple part of the Zariski closure of G has simple components only of type G2, F4 or E8 (and in this case indeed this can happened!)
Cite
@article{arxiv.1108.1044,
title = {Normal Subgroup Growth of Linear Groups: the (G2; F4;E8)-Theorem},
author = {Michael Larsen and Alexander Lubotzky},
journal= {arXiv preprint arXiv:1108.1044},
year = {2011}
}
Comments
This is an old paper, we upload it now in order for it to have an online access