The Number of Groups of a given Genus

DOI10.2307/1998288zbMath0444.05039OpenAlexW4245022112MaRDI QIDQ3887484

Thomas W. Tucker

Publication date: 1980

Full work available at URL: https://doi.org/10.2307/1998288

zbMATH Keywords

Cayley graphEuler characteristicRiemann surfacegenus of a groupnumber of groups of a given genus

Mathematics Subject Classification ID

Exact enumeration problems, generating functions (05A15) Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Relations of low-dimensional topology with graph theory (57M15)

Related Items (9)

Topological Graph Theory: A Personal Account ⋮ Maximal automorphism groups of symmetric Riemann surfaces with small genus ⋮ Nonorientable embeddings of groups ⋮ On the Genus of Symmetric Groups ⋮ A determination of the toroidalk-metacyclic groups ⋮ There is one group of genus two ⋮ Finite groups acting on surfaces and the genus of a group ⋮ The symmetric genus of alternating and symmetric groups ⋮ A refined Hurwitz theorem for embeddings of irredundant Cayley graphs

Cites Work

• Every connected regular graph of even degree is a Schreier coset graph
• Special embeddings of Cayley diagrams
• Voltage graphs
• Classification of the toroidal groups
• Cayley Diagrams on the Anchor Ring
• Unnamed Item
• Unnamed Item

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