arXiv subjects

J. Moritz Petschick

Publications and source records attributed to J. Moritz Petschick.

3 recordsLinked to original sources

arXiv2026

Representation zeta functions of split extensions of $SL_2^m(O)$

We consider the representation growth of split extensions of $SL_2^m(O)$. We prove that the corresponding representation zeta functions factor as a product of the representation zeta function of $SL_2^m(O)$ and the relative representation zeta function associated to the extension. We make use of our result by computing the zeta functions for two infinite families of split extensions of $SL_2^m(O)$ explicitly. Along the way, we compute the representation zeta functions of a large class of subgroups of $SL_2^m(O)$.

math.GR↗

arXiv2025

Branch groups with many maximal subgroups

This article presents the construction of finitely generated branch groups with uncountably many maximal subgroups using embedding techniques. This addresses a question posed by Grigorchuk.

math.GR↗

arXiv2024

Maximal subgroups in torsion branch groups

We study the maximal subgroups of branch groups and obtain a criterion that ensures that certain spinal groups are contained in the class $\mathcal{MF}$ of groups with all maximal subgroups of finite index. This allows us to construct branch groups within $\mathcal{MF}$ exhibiting novel properties, for example groups that possess non-normal maximal subgroups. Furthermore, we give new concrete examples of branch groups outside $\mathcal{MF}$, with explicitly given maximal subgroups of infinite index. Most prominently, we construct a periodic branch group outside $\mathcal{MF}$.

math.GR↗