Commutator subgroups of generalized Hecke and extended generalized Hecke groups,II

Abstract

Let $p_{1},\ \cdots,\ p_{n}$ be integers where $n\geq 2$ and each $p_{i} \geq 2$. Let also $H(p_{1},\ \cdots,\ p_{n})$ be the generalized Hecke group associated to all $p_{i}\geq 2.$ In this paper, we study the commutator subgroups $H^{\prime}(p_{1},\ \cdots,\ p_{n})$ and $\overline{H}^{\prime }(p_{1},\ \cdots,\ p_{n})$ of the generalized Hecke group $H(p_{1},\ \cdots,\ p_{n})$ and the extended generalized Hecke group $\overline{H}% (p_{1},\ \cdots,\ p_{n})$. We give the generators and the signatures of $% H^{\prime}(p_{1},\ \cdots,\ p_{n})$ and $\overline{H}^{\prime}(p_{1},\ \cdots,\ p_{n})$.