# Generators and relations for discrete groups

@inproceedings{Coxeter1957GeneratorsAR, title={Generators and relations for discrete groups}, author={H. S. M. Coxeter and William O. J. Moser}, year={1957} }

1. Cyclic, Dicyclic and Metacyclic Groups.- 2. Systematic Enumeration of Cosets.- 3. Graphs, Maps and Cayley Diagrams.- 4. Abstract Crystallography.- 5. Hyperbolic Tessellations and Fundamental Groups.- 6. The Symmetric, Alternating, and other Special Groups.- 7. Modular and Linear Fractional Groups.- 8. Regular Maps.- 9. Groups Generated by Reflections.- Tables 1-12.

## 1,934 Citations

### Finite metacyclic groups acting on bordered surfaces

- MathematicsGlasgow Mathematical Journal
- 1994

A group is called metacyclic in case both its commutator subgroup and commutator quotient group are cyclic. Thus a metacyclic group is a cyclic extension of a cyclic group, and metacyclic groups are…

### Twisted Conjugacy for Virtually Cyclic Groups and Crystallographic Groups

- Mathematics
- 2010

A group is said to have the property R ∞ if every automorphism has an infinite number of twisted conjugacy classes. In this paper, we classify all virtually cyclic groups with the R ∞ property.…

### Explicit resolutions for the binary polyhedral groups and for other central extensions of the triangle groups

- Mathematics
- 1983

This paper will exhibit two classes of finitely presented groups for which explicit free resolutions can be obtained by direct algebraic calculations. The resolutions will be either periodic of…

### Connectivity and planarity of power graphs of finite cyclic, dihedral and dicyclic groups

- Mathematics
- 2014

The power graph of a finite group is the graph whose vertices are the elements of the group and two distinct vertices are adjacent if and only if one is an integral power of the other. In this paper…

### Matroid Automorphisms and Symmetry Groups

- MathematicsCombinatorics, Probability and Computing
- 2000

All possible automorphism groups of MW are determined and when W ≅ = Aut(MW) is determined, which allows us to connect combinatorial and geometric symmetry.

### Generators and integrity bases for some point groups

- Mathematics
- 1972

Several results concerning the generators of point groups are discussed. The rank of C3h, D3 and other point groups is investigated by showing their Cayley diagrams to be isomorphic to directed…

### 359-Multiplicative Dedekind ~-function and representations of finite groups

- Mathematics
- 2005

In this article we study the problem of finding such finite groups that the modular forms associated with all elements of these groups by means of a certain faithful representation belong to a…

### The non-orientable genus of some metacyclic groups

- MathematicsComb.
- 1992

AbstractWe describe non-orientable, octagonal embeddings for certain 4-valent, bipartite Cayley graphs of finite metacyclic groups, and give a class of examples for which this embedding realizes the…