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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.
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.
Textbook accounts on group presentations:
David Lawrence Johnson, Topics in Theory of Group Presentations, London Mathematical Society Lecture notes series 42, Cambridge Univ. Press (1980) [doi:10.1017/CBO9780511629303]
David Lawrence Johnson, Presentations of Groups, London Mathematical Society Student Texts 15, Cambridge Univ. Press (1990) [doi:10.1017/CBO9781139168410]
Lecture notes:
On (finitely) presented groups as fundamental groups of (finite) simplicial complexes/CW-complexes:
Joseph J. Rotman, around Thm. 7.34 in: An Introduction to Algebraic Topology, Graduate Texts in Mathematics 119 (1988) $[$doi:10.1007/978-1-4612-4576-6$]$
Behrooz Mashayekhy, Hanieh Mirebrahimi, Some Properties of Finitely Presented Groups with Topological Viewpoints, International Journal of Mathematics, Game Theory and Algebra 18 6 (2010) 511-515 [arXiv:1012.1744]
Last revised on February 3, 2023 at 07:55:26. See the history of this page for a list of all contributions to it.