Peter Muller

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math.GR2026

A note about Jordan's bound on the size of finite linear groups

Peter MÃ¼ller

In 1878 Camille Jordan showed that every finite subgroup $G \leq GL_{n} (C)$ has an abelian normal subgroup $A$ such that $∣ G / A ∣$ is bounded in terms of $n$ , bu…

math.GR2025

Transitive sets of derangements in primitive actions of PSL_2(q)

Peter MÃ¼ller

Problem 8.75 of the Kourovka Notebook [10], attributed to John G. Thompson, asks the following: Suppose $G$ is a finite primitive permutation group on $I^c ◯$ , and $I^\pm$ , $I^^{2}$ are dist…

math.GR2025

Normal subgroups and permutation characters: a correction to a proof of Klingen

Peter Muller, Pablo Spiga

Let $G$ be a finite group. For subgroups $U$ and $V$ let $1_{U}^{G}$ and $1_{V}^{G}$ be the permutation characters for the action of $G$ on the right cosets of $U$ and $V$ , respectively. L…