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- Title
Spectral Analysis of the Adjacency Matrices for Alternating Quotients of Hyperbolic Triangle Group ▵ * (3, q , r) for q < r Primes.
- Authors
Younas, Sajida; Kousar, Sajida; Albaity, Majed; Mahmood, Tahir
- Abstract
Hyperbolic triangle groups are found within the category of finitely generated groups. These are topological groups formed by the reflections along the sides of a hyperbolic triangle and acting properly discontinuously on the hyperbolic plane. Higman raised a question about the simplicity of finitely generated groups. The best known example of a simple group is the alternating group A n , where n ≥ 5 . This article establishes a relation between the hyperbolic triangle group denoted as ▵ * (3 , 7 , r) and the alternating group. The approach involves employing coset diagrams to establish this connection. The construction of adjacency matrices for these coset diagrams is performed, followed by a detailed examination of their spectral characteristics.
- Subjects
HYPERBOLIC groups; TRIANGLES; TOPOLOGICAL groups
- Publication
Axioms (2075-1680), 2023, Vol 12, Issue 12, p1128
- ISSN
2075-1680
- Publication type
Article
- DOI
10.3390/axioms12121128