A finitely presented group is a group with a finite
number of generators and relations.
A mathematical joke involving finitely presented groups is given by Renteln and Dundes (2005).
Q: What's purple, round, and doesn't get much for Christmas? A: A finitely presented grape.
A group is of type 
when it admits a classifying
space with finitely many cells in each dimension.
See also
Amenable Group,
Burnside Problem,
Classifying Space,
Group
Presentation,
Group Word Problem
Portions of this entry contributed by David
Terr
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References
Renteln, P. and Dundes, A. "Foolproof: A Sampling of Mathematical Folk Humor." Notices Amer. Math. Soc. 52, 24-34,
2005.Referenced on Wolfram|Alpha
Finitely Presented Group
Cite this as:
Weisstein, Eric W., with contributions by David Terr. "Finitely Presented Group." From MathWorld--A
Wolfram Resource. https://mathworld.wolfram.com/FinitelyPresentedGroup.html
Subject classifications
