Finite groups acting on surfaces and the genus of a group

DOI10.1016/0095-8956(83)90009-6zbMath0521.05027OpenAlexW1991490328MaRDI QIDQ1055423

Thomas W. Tucker

Publication date: 1983

Published in: Journal of Combinatorial Theory. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0095-8956(83)90009-6

zbMATH Keywords

Cayley graphs2-manifoldgenusbranched coveringssymmetric genusVoltage graph

Mathematics Subject Classification ID

Planar graphs; geometric and topological aspects of graph theory (05C10) Graphs and abstract algebra (groups, rings, fields, etc.) (05C25) Fuchsian groups and their generalizations (group-theoretic aspects) (20H10)

Related Items (45)

FINITE, FIBER- AND ORIENTATION-PRESERVING ACTIONS ON ORIENTABLE SEIFERT MANIFOLDS WITH NON-ORIENTABLE BASE SPACE ⋮ On the cohomology of the hyperelliptic mapping class group ⋮ Split metacyclic actions on surfaces ⋮ Maximal automorphism groups of symmetric Riemann surfaces with small genus ⋮ On nilpotent orientably-regular maps of nilpotency class \(4\) ⋮ The symmetric genus of metacyclic groups ⋮ On the genus of \({\mathbb{Z}}_ 3\times {\mathbb{Z}}_ 3\times {\mathbb{Z}}_ 3\) ⋮ Covalence sequences of planar vertex-homogeneous maps ⋮ On a canonical construction of tessellated surfaces from finite groups ⋮ (2,3,_p)-generations for the fischer group f₂₂ ⋮ Finite metacyclic groups acting on bordered surfaces ⋮ Cellular automorphisms and self-duality ⋮ Regular maps with almost Sylow-cyclic automorphism groups, and classification of regular maps with Euler characteristic \(-p^{2}\) ⋮ Regular Cayley maps of elementary abelian \(p\)-groups: classification and enumeration ⋮ Groups of small symmetric genus ⋮ Finite symmetries of surfaces of p-groups of co-class 1 ⋮ On planar Cayley graphs and Kleinian groups ⋮ Commuting conjugates of finite-order mapping classes ⋮ The equisymmetric stratification of the moduli space and the Krull dimension of mapping class groups ⋮ Finite actions on the 2-sphere, the projective plane and I-bundles over the projective plane ⋮ The Groups of Symmetric Genus σ ≤ 8 ⋮ THE SYMMETRIC GENUS OF 2-GROUPS ⋮ THE 2-GROUPS OF ODD STRONG SYMMETRIC GENUS ⋮ An update on Hurwitz groups ⋮ Some results on quotients of triangle groups ⋮ The strong symmetric genus of the finite Coxeter groups ⋮ On the Farrell cohomology of the mapping class group of non-orientable surfaces ⋮ The Symmetric Genus of Sporadic Groups ⋮ The Homology and Higher Representations of the Automorphism Group of a Riemann Surface ⋮ Classification of regular maps of negative prime Euler characteristic ⋮ On the Farrell cohomology of mapping class groups ⋮ Groups \(\mathrm{PSL}(3,p)\) and nonorientable regular maps. ⋮ Regular dessins d'enfants with dicyclic group of automorphisms ⋮ Classifying finite group actions on surfaces of low genus ⋮ Tilings of the Torus and the Klein Bottle and Vertex-Transitive Graphs on a Fixed Surface ⋮ THE STRONG SYMMETRIC GENUS OF DIRECT PRODUCTS ⋮ Surface symmetries and $PSL_2(p)$ ⋮ There is one group of genus two ⋮ Cayley maps ⋮ A note on Cayley graphs ⋮ The symmetric genus of alternating and symmetric groups ⋮ A refined Hurwitz theorem for embeddings of irredundant Cayley graphs ⋮ Embeddings of graphs ⋮ Finite groups acting on bordered surfaces and the real genus of a group ⋮ The Symmetric Genus of p-Groups

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Surfaces and planar discontinuous groups. Revised and expanded transl. from the German by J. Stillwell
• On the genus of finite abelian groups
• Generating all graph coverings by permutation voltage assignments
• Special embeddings of Cayley diagrams
• Classification of the toroidal groups
• On a Class of Fixed-Point-Free Graphs
• Generators for Alternating and Symmetric Groups
• The Number of Groups of a given Genus
• Some results on the genus of a group
• The Plane Symmetry Groups: Their Recognition and Notation
• Theory of Maps on Orientable Surfaces
• Abelian Groups of Automorphisms of Compact Riemann Surfaces
• The Classification of Non-Euclidean Plane Crystallographic Groups
• Automorphisms of compact non-orientable Riemann surfaces
• On the Genus of a Group

This page was built for publication: Finite groups acting on surfaces and the genus of a group