I am asking purely out of interest: What the abelianization of general linear group $GL(n,\mathbb{R})$?
2026-03-26 01:00:28.1774486828
Abelianization of general linear group?
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The derived group of ${\rm GL}(n,K)$ is ${\rm SL}(n,K)$ for all $n \ge 1$ and all fields $K$, so the abelianization of ${\rm GL}(n,K)$ is the multiplicative group of the field, $(K \setminus \{0\},\times)$.