Let $ (V,q)$ a quadratic space over a finite field. The normal subgroup $ \Omega(V)\subset SO(V)$ can be defined as the commutator subgroup of $ O(V)$ (or $ SO(V)$ ). In characteristic two the group cohomology $ H^2(\Omega(V), V)$ does not vanish
Griess, Robert L.jun., Automorphisms of extra special groups and nonvanishing degree 2 cohomology, Pac. J. Math. 48, 403-422 (1973). ZBL0283.20028.
Is it true that $ H^2(\Omega(V), V)=0$ for any quadratic space in a finite field of odd characteristic? Thanks.
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