  It is shown that there exist infinitely many non-integers $r>2$ such that the
Dehn function of some finitely presented group is $\simeq n^r$. For each
positive rational number $s$ we construct pairs of finitely presented groups
$H\subset G$ such that the distortion of $H$ in $G$ is $\simeq n^s$. And for
each $s\ge 1$ we also construct finitely presented groups whose isodiametric
function is $\simeq n^s$.
