nLab finitely presentable group

Finitely presented groups


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


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.


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.