Turkish Journal of Mathematics
Abstract
Let $q\geq 3$ be a prime number and let $\overline{H}(\lambda _{q})$ be the extended Hecke group associated with $q.$ In this paper, we determine the presentation of the commutator subgroup ($H$($\lambda _{q})\alpha )^{\prime } $ of the normal subgroup $H$($\lambda _{q})\alpha $, where $H$($\lambda _{q})\alpha $ is a subgroup of index $2$ in $\overline{H}$($\lambda _{q}).$ Next we discuss the commutator subgroup ($\overline{H}_{2})^{\prime }$($% \lambda _{q})$ of the principal congruence subgroup $\overline{H}_{2}$($% \lambda _{q})$ of $\overline{H}$($\lambda _{q})$. Then we show that some quotient groups of $\overline{H}$($\lambda _{q})$ are generalized $M^{\ast }- $groups. Finally, we prove some results related to some normal subgroups of $\overline{H}$($\lambda _{q})$, especially in the case $q=5.$
DOI
10.3906/mat-1704-81
Keywords
Extended Hecke groups, commutator subgroups, principal congruence subgroups, generalized $M^{\ast }-$groups
First Page
621
Last Page
632
Recommended Citation
ŞAHİN, R (2018). Some results on Hecke and extended Hecke groups. Turkish Journal of Mathematics 42 (2): 621-632. https://doi.org/10.3906/mat-1704-81
