Suppose $G, H$ be two groups such that $G$ is finitely presented(with number of defining relators must be at least 1) and let $\phi$ : $G \rightarrow$ $H$ be an epimorphism. Does it imply that $H$ a finitely presented group?
2026-03-26 05:54:23.1774504463
Quotient of finitely presented group
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A method for constructing an example which shows that the answer is negative (see for instance this reference) is to go for a finitely presented group $G$ whose centre $Z(G)$ is not finitely generated. Then, by a standard result (which I think has been recorded by Bernhard Neumann), $G/Z(G)$ is not finitely presented.