= Unipotent involutions in characteristic two
{title2=$g=I+N,\quad N^2=0$}
An involution in characteristic two has Jordan blocks of sizes at most two. Its conjugacy type is determined by the rank of $N$, subject to $2\operatorname{rank}N\le\dim V$. GL-conjugacy can split in SL if the centralizer determinant map is not onto; that issue must be checked separately. In $SL_3(4)$ a one-dimensional untouched block makes that determinant map onto, yielding one involution class. In $SL_4(2)=GL_4(2)$ the two possible nonzero ranks give two classes. Their projective quotients have equal order but different involution class counts.
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