# Finitely presented groups

## Idea

A group $G$ is finitely presentable if it has a finite presentation, i.e., there is a group presentation, $\langle X: R\rangle$, for $G$ with both its set, $X$, of generators and its set, $R$, of relations being finite sets.

###### Remark

The term ‘finitely presented’ is often used rather than `finitely presentable', however 'finitely presented' would seem to imply that a given finite presentation was intended, whilst here only the existence of one is required.

## References

Useful elementary or introductory texts, include

• D. L. Johnson, Presentations of Groups (London Mathematical Society Student Texts 15) 1990, Cambridge Univ. Press,

and the earlier:

• D. L. Johnson, Topics in Theory of Group Presentations, London Mathematical Society Lecture notes series 42) 1980, Cambridge Univ. Press.

Last revised on January 26, 2014 at 21:24:49. See the history of this page for a list of all contributions to it.