For any field $F$, it's known that the abelianization of $GL(n,F)$ is $F^{*}$ except for $GL(2,\mathbb{F}_{2})$. What is the abelianization of $PGL(n,F)$? It seems to me there are non-trivial elements in some cases but I cannot find good reference on it.
2026-03-26 09:41:12.1774518072
Abelianization of $PGL(n,F)$
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