Adjacency matrices of \(PSL(2,5)\) and resemblance of its coset diagrams with fullerene \(C_{60}\). (English) Zbl 1274.05259
Summary: The action of \(PSL(2,\mathbb Z)\) on \(PL(F_{5^{n}})\) yields \(PSL(2,5)\). In this paper, we use the adjacency matrices of the abstract group \(PSL(2,5)\), eventually of fullerene \(C_{60}\), to draw the coset diagram and investigate various properties of the diagram with reference to the intransitivity of the action and the number of orbits.
MSC:
| 05C38 | Paths and cycles |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
| 20C30 | Representations of finite symmetric groups |
Keywords:
adjacency matrices; \(PSL(2,5)\); coset diagrams; fullerene \(C_{60}\); pollakis polyhedral group; triangle groups; block diagonal matricesReferences:
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