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In this paper, we study the singularities of a general hyperplane section 
$H$ of a three-dimensional quasi-projective variety 
$X$ over an algebraically closed field of characteristic 
$p>0$. We prove that if 
$X$ has only canonical singularities, then 
$H$ has only rational double points. We also prove, under the assumption that 
$p>5$, that if 
$X$ has only klt singularities, then so does 
$H$.
