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Let $G$ be a connected reductive algebraic group over an algebraically closedfield $\mathbf{k}$, and let Lie$(G)$ be its associated Lie algebra. In hisseries of papers on unipotent elements in small characteristic, Lusztig defineda partition of the unipotent variety of $G$. This partition is very useful whenworking with representations of $G$. Equivalently, one can consider certainsubsets of the nilpotent variety of Lie$(G)$ called pieces. This approachappears in Lusztig's article from 2011. The pieces for the exceptional groupsof type $G_2$, $F_4$, $E_6$, $E_7$, and $E_8$ in bad characteristic have notyet been determined. This article presents a solution, relying on computationaltechniques, to this problem for groups of type $G_2$, $F_4$, and $E_6$.

On the computation of the nilpotent pieces in bad characteristic for algebraic groups of type $G_2$, $F_4$, and $E_6$