Strictly upper triangular

Theorem. Let G be a group consisting of unipotent matrices. Then in some basis all elements of G are strictly upper triangular (i.e., zero below the diagonal and 1 on the diagonal). 

Proof. After conjugation, the group will be inside the group U (fc) of all strictly upper triangular matrices. All elements of U (fc) are unipotent, and U (fc) is closed. ... 

In any closed embedding of G in GL , some element of GL (fc) conjugates G to a closed subgroup of the strict upper triangular group U . 

Sheaf in fpqc topology 117 Smooth group scheme 88 Solvable group scheme 73 Spec A 41 Split torus 56 Strictly upper triangular 62 Subcomodule 23 Symplectic group 99... 

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