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×.
Read more about this topic: Special Linear Group
Famous quotes containing the word structure:
“... the structure of a page of good prose is, analyzed logically, not something frozen but the vibrating of a bridge, which changes with every step one takes on it.”
—Robert Musil (1880–1942)