A₅ as a Homomorphic Image of a Subgroup of Picard Group

Abstract

In this article we investigate that what actions of a subgroup G ₁ of Picard group yield A ₅ = PSL(2, 5). We draw coset diagrams (propounded by G. Higman) for the action of G ₁ on finite fields PL(F _{5 ⁿ} ). The projective special linear groups PSL(2, p) when p = 5 can be seen as 5-multiples of tetrahedral rotation point group. It has applications in carbon chemistry and physics as PSL(2, 5) is the rotation group of the fullerene C ₆₀.

Key Words:

• Bianchi groups
• Cayley graphs
• Coset diagrams
• Fibonacci numbers
• Picard group

2000 Mathematics Subject Classification:

• Primary 05C38, 15A15
• Secondary 05A15, 15A18

Notes

Communicated by V. A. Artamonov.