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Nov 12, 2013 at 14:55 comment added abx By definition $SL_n(F)$ is the kernel of $\det: GL_n(F)\rightarrow F^*$, so $\det$ provides an isomorphism $GL_n(F)/SL_n(F){\buildrel {\sim}\over {\longrightarrow}}F^*$.
Nov 12, 2013 at 13:20 history answered abx CC BY-SA 3.0