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YCor
YCor
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Abelianization of $GL_n$\mathrm{GL}_n(\mathbb{Z})$

What$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SL{SL}$What is the abelianization of $GL_n(\mathbb{Z})$$\GL_n(\mathbb{Z})$? I know the abelianzation of $GL_n(\mathbb{F})$$\GL_n(\mathbb{F})$ where $\mathbb{F}$ is a field and the abelianization of $ SL_n(\mathbb{Z})$$ \SL_n(\mathbb{Z})$. However I can't find the abelianization of $GL_n(\mathbb{Z})$$\GL_n(\mathbb{Z})$ and I suspect this is something that should be well-known.

Abelianization of $GL_n(\mathbb{Z})$

What is the abelianization of $GL_n(\mathbb{Z})$? I know the abelianzation of $GL_n(\mathbb{F})$ where $\mathbb{F}$ is a field and the abelianization of $ SL_n(\mathbb{Z})$. However I can't find the abelianization of $GL_n(\mathbb{Z})$ and I suspect this is something that should be well-known.

Abelianization of $\mathrm{GL}_n(\mathbb{Z})$

$\DeclareMathOperator\GL{GL}\DeclareMathOperator\SL{SL}$What is the abelianization of $\GL_n(\mathbb{Z})$? I know the abelianzation of $\GL_n(\mathbb{F})$ where $\mathbb{F}$ is a field and the abelianization of $ \SL_n(\mathbb{Z})$. However I can't find the abelianization of $\GL_n(\mathbb{Z})$ and I suspect this is something that should be well-known.

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Marcos
Marcos
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Abelianization of $GL_n(\mathbb{Z})$

What is the abelianization of $GL_n(\mathbb{Z})$? I know the abelianzation of $GL_n(\mathbb{F})$ where $\mathbb{F}$ is a field and the abelianization of $ SL_n(\mathbb{Z})$. However I can't find the abelianization of $GL_n(\mathbb{Z})$ and I suspect this is something that should be well-known.