Title: Fractional isoperimetric inequalities and subgroup distortion
Abstract: It is shown that there exist infinitely many non-integers $r>2$ such that the Dehn function of some finitely presented group is $\simeq n^r$. Explicit examples of such groups are constructed. For each rational number $s\ge 1$ pairs of finitely presented groups $H\subset G$ are constructed so that the distortion of $H$ in $G$ is $\simeq n^s$.