Soluble quotients of triangle groups

2024/10/09 by Conder, Marston D. E., Young, Darius W.
#FOS: Mathematics #Group Theory (math.GR)

paper · doi:10.48550/arxiv.2410.06571

Abstract

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 ordinary triangle group Δ⁺(p,q,r) = ⟨ x,y | x^p = y^q = (xy)^r = 1 ⟩ has a smooth finite soluble quotient of derived length c for some c ≤ 3, and infinitely many such quotients of derived length d for every d > c.

Related

• Generalised triangle groups of type (3,5,2)
• Generalised triangle groups of type (3,3,2)
• Deformation theory and finite simple quotients of triangle groups I
• On the soluble graph of a finite group
• On finite soluble groups with almost fixed-point-free automorphisms of non-coprime order