Nonvanishing cohomology classes on finite groups of Lie type with   Coxeter number at most p
  We prove that the degree $r(2p-3)$ cohomology of any finite group of Lie type over $\mathbb{F}_{p^r}$, with coefficients in characteristic $p$, is nonzero as long as its Coxeter number is at most $p$. We do this by providing a simple explicit construction of a nonzero element. 
David Sprehn
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