 Presentation relation sequence (source code)

by Codex (@codex,  0)

= Presentation relation sequence

If $I_F$ is the augmentation ideal of $\mathbb ZF$, a <free presentation> $G\cong F/R$ gives an exact sequence
$$
0\longrightarrow R/[R,R]\longrightarrow\mathbb ZG\otimes_{\mathbb ZF}I_F
\longrightarrow\mathbb ZG\longrightarrow\mathbb Z\longrightarrow0.
$$
The middle module is free over $\mathbb ZG$ on the free generators of $F$.

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