Special Linear Group - Structure of GL(n,F)

Structure of GL(n,F)

The group GL(n, F) splits over its determinant (we use F× ≅ GL(1, F) → GL(n, F) as the monomorphism from F× to GL(n, F), see semidirect product), and therefore GL(n, F) can be written as a semidirect product of SL(n, F) by F×:

GL(n, F) = SL(n, F) ⋊ F×.

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