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YCor
YCor
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If $0\mapsto A \mapsto B \mapsto C\mapsto 0$$0\to A \to B \to C\to 0$ is a short exact sequence of groups and $A$, $C$ are of type $FP_{n}$, then so is $B$ (https://arxiv.org/pdf/1611.03759.pdf Prop. Reference: Proposition 2.2 in Homological finiteness properties of fibre products by Kochloukova and Ferreira Lima (arXiv link).

If $0\mapsto A \mapsto B \mapsto C\mapsto 0$ is a short exact sequence and $A$, $C$ are of type $FP_{n}$, then so is $B$ (https://arxiv.org/pdf/1611.03759.pdf Prop 2.2).

If $0\to A \to B \to C\to 0$ is a short exact sequence of groups and $A$, $C$ are of type $FP_{n}$, then so is $B$. Reference: Proposition 2.2 in Homological finiteness properties of fibre products by Kochloukova and Ferreira Lima (arXiv link).

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J.L.
J.L.
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If $0\mapsto A \mapsto B \mapsto C\mapsto 0$ is a short exact sequence and $A$, $C$ are of type $FP_{n}$, then so is $B$ (https://arxiv.org/pdf/1611.03759.pdf Prop 2.2).