  The authors classify the finite index subgroups of R. Thompson's group
  $F$. All such groups that are not isomorphic to $F$ are non-split extensions
of finite cyclic groups by $F$. The classification describes precisely which
finite index subgroups of $F$ are isomorphic to $F$, and also separates the
isomorphism classes of the finite index subgroups of $F$ which are not
isomorphic to $F$ from each other; characterizing the structure of the
extensions using properties of the structure of the finite index subgroups of
$Z\times Z$.
