Abstract—Quadratic fields are a basic object of study and class of examples in algebraic number theory. While we look at group acting on a set, we hope to gain insight into the symmetry of set, at the same time, to obtain a better feel for the group. Group actions on fields have diverse applications in physics, symmetries, algebraic geometry and cryptology. Congruence is nothing more than a statement of divisibility. However, it often helps to discover proofs and it suggests new ideas to solve the problems. Therefore the congruence classes have been used to explore the action of Möbius groups on quadratic fields. We investigate some proper subgroups of the Mobius group
Index Terms—Congruence, group action, linear transformations, mobius groups, quadratic fields.
Farkhanda Afzal is with the School of Mathematics and System Sciences, Beihang University, Beijing, China. (e-mail: farkhanda_imran@live.com).
Qamar Afzal and M. Aslam Malik are with the Department of Mathematics, University of Education, Okara, Pakistan. (e-mail: qamarafzal.edu@gmail.com, aslampu786@gmail.com).
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Cite:Farkhanda Afzal, Qamar Afzal, and M. Aslam Malik, "Quadratic Fields under the Action of Subgroups of M," International Journal of Modeling and Optimization vol. 3, no. 3, pp. 283-287, 2013.
