Evolution of ambiguous numbers under the actions of a Bianchi group. Issue 1 (1st January 2020)

• Record Type: Journal Article
• Authors: Yousaf, Awais; Alolaiyan, Hanan; Razaq, Abdul; Younis, Muhammad
• Is Part Of: Journal of Taibah University for science. Volume 14:Issue 1(2020)
• Page Start: 615
• Page End: 620
• Publication Date: 2020-01-01
• Subjects: Group action -- Bianchi group -- biquadratic irrational field -- orbits; Primary 05C25 -- Secondary 20H20; Science -- Periodicals; Science; Periodicals; 505
• DOI: 10.1080/16583655.2020.1760511
• Languages: English
• ISSNs: 1658-3655

Abstract

Abstract : In this paper we study some combinatorial properties of biquadratic irrational number field Q ( i, 3 ), under the action of a Bianchi group Γ 3 = P S L ( 2, O 3 ) . In this experiment it is revealed that a special class of elements exists; that is, for an element ξ its conjugate ξ ¯ has different signs in the closed path (orbits) for the action of Γ 3 over Q ( i, 3 ), known as ambiguous numbers. It is also proved that the orbit Γ ξ defined on a finite number of ambiguous numbers succeeding a unique closed path.