Normal Subgroup Growth of Linear Groups: the (G2; F4;E8)-Theorem

Details Normal Subgroup Growth of Linear Groups: the (G2; F4;E8)-Theorem Normal Subgroup Growth of Linear Groups: the (G2; F4;E8)-Theorem

2011-08-04

arxiv.org/abs/1108.1044v1

Algebraic Groups and Arithmetic (Mumbai 2001), Ed. S. G. Dani and G. Prasad, Tana Inst. Fund. Res. Stud. Math. pp. 441-468, TI

Mathematics

Group Theory

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Scientific paper

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!)

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