Suppose that $G$ is an absolutely quasi-simple algebraic group defined over a non-archimedean local field $k$ of positive characteristic. Would there be any kind of reasonable sufficient condition for $[G(k),G(k)]$ to have nonempty interior in the strong topology? I have already asked this question in the anistropic case and the answer seems to be affirmative there. I thought that I had a proof in the isotropic case but it seems to be mistaken. It has been suggested to me that making the assumption that $G$ is simply connected might be enough. Any hints for an extra hypothesis that might do the trick would be very helpful.