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Nonparabolic subgroups of the modular group

Published online by Cambridge University Press:  18 May 2009

Carol Tretkoff
Carol Tretkoff
Affiliation:
Courant Institute of Mathematical Sciences, 251 Mercer Street, New York, New York 10012
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In this paper we shall discuss maximal nonparabolic and maximal normal nonparabolic subgroups of the modular group Г = 〈ω, φ; ω2 =φ3 = 1〉. The modular group may also be defined as the group of fractional linear transformations w = (az+b)/(cz+d), where a, b, c, d are rational integers with ad − bc = 1. Here, a maximal nonparabolic subgroup of Г is a subgroup that contains no parabolic elements and any proper subgroup of Г which contains S contains parabolic elements. Similarly, a maximal normal nonparabolic subgroup is a normal nonparabolic subgroup of Г which is not contained in any larger normal nonparabolic subgroup of Г.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 16 , Issue 2 , September 1975 , pp. 91 - 102
Copyright
Copyright © Glasgow Mathematical Journal Trust 1975

References

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