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arXiv · 2410.06571

Soluble quotients of triangle groups

Marston D. E. Conder·Darius W. Young
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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 $\Delta^+(p,q,r) = \langle\, x,y \ | \ x^p = y^q = (xy)^r = 1 \,\rangle$ has a smooth finite soluble quotient of derived length $c$ for some $c \le 3$, and infinitely many such quotients of derived length $d$ for every $d > c$.

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Marston D. E. Conder, Darius W. Young. 2024-10-09. Soluble quotients of triangle groups. https://arxiv.org/abs/2410.06571

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