Stratified bundles and \'etale fundamental group

v2: A few typos corrected, a few formulations improved. On $X$ projective smooth over an algebraically closed field of characteristic $p>0$, we show that irreducible stratified bundles have rank 1 if and only if the commutator $[{\pi }_1^{\acute{\mathrm{e}}\mathrm{t}},{\pi }_1^{\acute{\mathrm{e}}\mathrm{t}}]$ of the 'etale fundamental group is a pro-$p$-group, and we show that the category of stratified bundles is semi-simple with irreducible objects of rank 1 if and only if ${\pi }_1^{\acute{\mathrm{e}}\mathrm{t}}$ is abelian without $p$-power quotient. This answers positively a conjecture by Gieseker.