The normal growth of linear groups over formal power serieses

Abstract

Put $R=\F[[t_1, \ldots, t_d]])$. We estimate the number of normal subgroups of $\mathrm{SL}_2^1(\F[[t_1, \ldots, t_d]])$ for $p>2$, the number of ideals in the Lie algebra $\Lie(R)$, and the number of ideals in the associative algebra $R$.

This is a preliminary version. The final version will treat more general algebraic groups, and generalize normal subgroups to subgroups with large normalizer