Principal congruence subgroups of the Hecke groups and related results (Q1041285)

The authors, determine the quotient groups of the Hecke groups \(H(\lambda_q)\) for prime \(q\geq 7\), by their principal congruence subgroups \(H_p(\lambda_q)\) of level \(p\) where \(p\) is prime. Then, they give the principal congruence subgroups of the extended Hecke groups \(\overline{H} (\lambda_q)\) for prime \(q\geq 5\). Also they showed that some of the quotient groups of the Hecke group \(H(\lambda_q)\) and the extended Hecke group \(\overline{H}(\lambda_q)\) for prime \(q\geq 5\), by their principal congruence subgroups \(H_p(\lambda_q)\) are \(M^*\)-groups.