Peter Muller

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20032026

most citedPermutation groups of prime degree, a quick proof of Burnside's theorem

13 citations · 17 across the 7 of their papers we have counts for

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math.GR2026

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

Peter Müller

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 Müller

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 $Ω$ , and $α$ , $β$ are distinc…

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…

math.GR2024

A note about solvable and non-solvable finite groups of the same order type

Peter Müller

Two finite groups are said to have the same order type if for each positive integer $n$ both groups have the same number of elements of order $n$ . In 1987 John G. Thompson asked if…

math.GR2003★ 13 cited

Permutation groups of prime degree, a quick proof of Burnside's theorem

Peter Müller

A transitive permutation group of prime degree is doubly transitive or solvable. We give a direct proof of this theorem by Burnside which uses neither S-ring type arguments, nor re…