3 papers
math.GR2026
A note on the reflexibility of regular maps with automorphism group PGL(2,q)
Darius W. Young
By a short adaptation of an argument of Singerman, we show that for every prime power , every orientably regular map (or hypermap) whose orientation-preserving automorphism grou…
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…
math.GR2024
Soluble quotients of triangle groups
Marston D. E. Conder, Darius W. Young
This paper helps explain the prevalence of soluble groups among the automorphism groups of regular maps (at least for `small' genus), by showing that every non-perfect hyperbolic o…