How to show that the radical of a reductive linear algebraic group is a torus $(\mathbb C^*)^n$?
2026-03-25 09:27:40.1774430860
The radical of an algebraic group is a torus
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A standard example of connected solvable group is the group of (upper) triangular non-singular matrices. This has a nice structure theorem: semi-direct product of torus with strictly upper triangular (i.e., 1's in the diagonal)
Lie-Kolchin theorem states that connected solvable groups are closed subgroups of the above.
Now unipotent radical is trivial hypothesis combined with the above should tell you that it is a torus.