Abstract
The derived series for all co-compact non-perfect Fuchsian groups are investigated. These groups are residually finite and residually soluble. The intersection of the derived series for these groups is the identity. We will show that if $\Gamma$ is not perfect, then the number of terms in the derived series up to and including the first surface group cannot exceed $4$. We then use this result to compute the derived series of some important general triangle groups.
Citation
Reza Zomorrodian. "Residual solubility of Fuchsian groups." Illinois J. Math. 51 (3) 697 - 703, Fall 2007. https://doi.org/10.1215/ijm/1258131097
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