The normal growth of linear groups over formal power serieses

Yiftach Barnea; Jan-Christoph Schlage-Puchta

The normal growth of linear groups over formal power serieses

Group Theory 2025-02-03 v1

Authors: Yiftach Barnea , Jan-Christoph Schlage-Puchta

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 $R$ .

Keywords

linear groups formal power series normal subgroups Lie algebra associative algebra

Cite

@article{arxiv.2501.19127,
  title  = {The normal growth of linear groups over formal power serieses},
  author = {Yiftach Barnea and Jan-Christoph Schlage-Puchta},
  journal= {arXiv preprint arXiv:2501.19127},
  year   = {2025}
}

Comments

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

The normal growth of linear groups over formal power serieses

Abstract

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