On maximal nonparabolic normal subgroups of the modular group
HTML articles powered by AMS MathViewer
- by A. W. Mason and N. K. Dickson PDF
- Proc. Amer. Math. Soc. 77 (1979), 167-173 Request permission
Abstract:
Let F be a free normal subgroup of finite index in the modular group $\Gamma$ with $F \ne \Gamma ’.F’$ is known to be a nonparabolic normal subgroup of $\Gamma$. We show that, with two exceptions, there exists another nonparabolic normal subgroup of $\Gamma$ properly containing $F’$.References
- Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0144979
- Daniel Gorenstein, Finite groups, Harper & Row, Publishers, New York-London, 1968. MR 0231903
- Donald McCarthy, Infinite groups whose proper quotient groups are finite. I, Comm. Pure Appl. Math. 21 (1968), 545–562. MR 237637, DOI 10.1002/cpa.3160210604
- W. Magnus, Rational representations of Fuchsian groups and non-parabolic subgroups of the modular group, Nachr. Akad. Wiss. Göttingen Math.-Phys. Kl. II (1973), 179–189. MR 346069
- A. W. Mason, Lattice subgroups of free congruence groups, Glasgow Math. J. 10 (1969), 106–115. MR 276365, DOI 10.1017/S0017089500000641
- A. W. Mason, Lattice subgroups of normal subgroups of genus zero of the modular group, Proc. London Math. Soc. (3) 24 (1972), 449–469. MR 304500, DOI 10.1112/plms/s3-24.3.449
- A. W. Mason and W. W. Stothers, Remarks on a theorem of L. Greenberg on the modular group, Pacific J. Math. 78 (1978), no. 2, 385–395. MR 519761
- Morris Newman, A complete description of the normal subgroups of genus one of the modular group, Amer. J. Math. 86 (1964), 17–24. MR 163966, DOI 10.2307/2373033
- Morris Newman, Integral matrices, Pure and Applied Mathematics, Vol. 45, Academic Press, New York-London, 1972. MR 0340283
- Paul E. Schupp, Embeddings into simple groups, J. London Math. Soc. (2) 13 (1976), no. 1, 90–94. MR 401932, DOI 10.1112/jlms/s2-13.1.90
- Carol Tretkoff, Nonparabolic subgroups of the modular group, Glasgow Math. J. 16 (1975), no. 2, 91–102. MR 399289, DOI 10.1017/S0017089500002573
Additional Information
- © Copyright 1979 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 77 (1979), 167-173
- MSC: Primary 20H05; Secondary 10D07, 20H10
- DOI: https://doi.org/10.1090/S0002-9939-1979-0542079-1
- MathSciNet review: 542079