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For $r \\geq 1$ define the Frobenius kernel, $G_r$, to be the kernel of $F$ iterated with itself $r$ times. Define $U_r$ (respectively $B_r$) to be the kernel of the Frobenius map restricted to $U$ (respectively $B$). 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Wright","submitted_at":"2008-09-17T00:47:42Z","abstract_excerpt":"Let $G$ be a simple simply connected algebraic group scheme defined over an algebraically closed field of characteristic $p > 0$. Let $T$ be a maximal split torus in $G$, $B \\supset T$ be a Borel subgroup of $G$ and $U$ its unipotent radical. Let $F: G \\rightarrow G$ be the Frobenius morphism. For $r \\geq 1$ define the Frobenius kernel, $G_r$, to be the kernel of $F$ iterated with itself $r$ times. Define $U_r$ (respectively $B_r$) to be the kernel of the Frobenius map restricted to $U$ (respectively $B$). 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