On Subsets of Q(√m) Q under the Action of Hecke Groups H(λ_{q})

Affiliation(s)

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan.

Center for Undergraduate Studies, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan.

Department of Mathematics, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan.

Center for Undergraduate Studies, University of the Punjab, Quaid-e-Azam Campus, Lahore, Pakistan.

Abstract

is the
disjoint union of for
all , where is the
set of all roots of primitive second degree equations , with reduced discriminant equal
to *k*^{2}m. We study the action of two Hecke groups—the full modular group and
the group of linear-fractional transformations on . In particular, we investigate the action of on for
finding different orbits.

Cite this paper

Malik, M. and Zafar, M. (2014) On Subsets of Q(√m) Q under the Action of Hecke Groups H(λ_{q}). *Applied Mathematics*, **5**, 1284-1291. doi: 10.4236/am.2014.58120.

Malik, M. and Zafar, M. (2014) On Subsets of Q(√m) Q under the Action of Hecke Groups H(λ

References

[1] Sahin, R. and Bizim, O. (2003) Some Subgroups of the Extended Hecke Groups . Mathematica Acta Scientia, 23B, 497-502.

[2] Mushtaq, Q. (1988) Modular Group Acting on Real Quadratic Fields. Bulletin of the Australian Mathematical Society, 3, 303-309.

[3] Husnine, S.M., Aslam Malik, M. and Majeed, A. (2005) On Ambiguous Numbers of an Invariant Subset of under the Action of the Modular Group PSL(2,Z). Studia Scientiarum Mathematicarum Hungarica, 42, 401-412.

http://dx.doi.org/10.1556/SScMath.42.2005.4.5

[4] Aslam Malik, M. and Asim Zafar, M. (2011) Real Quadratic Irrational Numbers and Modular Group Action. Southeast Asian Bulletin of Mathematics, 35, 439-445.

[5] Malik, M.A. and Asim Zafar, M. (2013) G-Subsets of an Invariant Subset of under the Modular Group Action. Utilitas Mathematica, 91, 377-387.

[6] Aslam Malik, M., Husnine, S.M. and Majeed, A. (2005) Intrasitive Action of the Modular Group on a Subset of . PUJM, 37, 31-38.

[7] Mushtaq, Q. and Aslam, M. (1997) Transitive Action of a Two Generator Group on Rational Projective Line. Southeast Asian Bulletin of Mathematics, 1, 203-207.

[8] Aslam Malik, M., Husnine, S.M. and Asim Zafar, M. (2012) Certain H-Subsets of under the Action of . Pakistan Journal of Science, 64, 67-74.