Subgroup growth in some profinite Chevalley groups

Capdeboscq, Inna; Kirkina, Karina; Rumynin, Dmitriy

doi:10.1090/proc/13567

Subgroup growth in some profinite Chevalley groups
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by Inna Capdeboscq, Karina Kirkina and Dmitriy Rumynin

Proc. Amer. Math. Soc. 145 (2017), 4187-4200

DOI: https://doi.org/10.1090/proc/13567

Published electronically: April 7, 2017

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Abstract:

In this article we improve the known uniform bound for subgroup growth of Chevalley groups $\mathbf {G}(\mathbb {F}_p[[t]])$. We introduce a new parameter, the ridgeline number $v(\mathbf {G})$, and give new bounds for the subgroup growth of $\mathbf {G}(\mathbb {F}_p[[t]])$ expressed through $v(\mathbf {G})$. We achieve this by deriving a new estimate for the codimension of $[U,V]$ where $U$ and $V$ are vector subspaces in the Lie algebra of $\mathbf {G}$.

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