Gabriel Verret

collaborators

5 papers

math.GR2025

Some new compatible groups

Zhaochen Ding, Gabriel Verret

Two finite groups $L_{1}$ and $L_{2}$ are compatible if there exists a finite group $G$ with isomorphic normal subgroups $N_{1}$ and $N_{2}$ such that $L_{1} ≅ G / N_{1}$ and $L_{2} ≅ G / N_{2}$ …

math.CO2025

On transitive permutation groups with exponential graph growth

ÄorÄe MitroviÄ, Gabriel Verret

Let $I^$ be a finite connected graph and $G$ a vertex-transitive group of its automorphisms. The pair $(I^, G)$ is said to be locally- $L$ if the permutation group induced by the ac…

math.GR2025

Derangements in permutation groups with two orbits

Melissa Lee, Tomasz Popiel, Gabriel Verret

A classical theorem of Jordan asserts that if a group $G$ acts transitively on a finite set of size at least $2$ , then $G$ contains a derangement (a fixed-point free element). Gene…

math.GR2025

Some necessary conditions for compatibility of groups

Zhaochen Ding, Gabriel Verret

Two groups $L_{1}$ and $L_{2}$ are compatible if there exists a finite group $G$ with isomorphic normal subgroups $N_{1}$ and $N_{2}$ such that $L_{1} ≅ G / N_{1}$ and $L_{2} ≅ G / N_{2}$ . In th…

math.GR2024

Density of quotient orders in groups and applications to locally-transitive graphs

Marston Conder, Gabriel Verret, Darius Young

We prove that the set of orders of finite quotients of a finitely generated group has natural density 0, 1/2 or 1, and characterise when each of these cases occurs. We apply this t…