Reflection Subgroups of the Maass-Hurwitz Groups

Student: Matveev Aleksandr

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2020

For a real quadratic field, we study the Maass-Hurwitz group and two of its subgroups, namely the Hilbert modular group and the extended Hilbert modular group. The aim of the work is to determine for which quadratic fields these groups are generated by reflections. We completely answer the question for two latter groups when the discriminant of the field is divisible by 4 and give an infinite sequence of fields with reflective Maass-Hurwitz group.

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